NTIA-REPORT-79-26

Switch Element Capacities

in Access Area Digital

Switching Systems

R. F. Linfield

M. Nesenbergs

Prepared for

U.S. Army Communications Systems: Agency

Ft. Monmouth, New Jersey 07703

u.s. DEPARTMENT OF COMMERCE

Juanita M. Kreps, Secretary

Henry Geller, Assistant Secretary

for Communications and Information

September 1979
DISCLAIMER

The views, oplnlons, and/or findings contained in this

report are those of the authors and should not be construed

as an official Department of the Army position, policy, or

decision unless designated by other official documentation.

; i
PREFACE

The study reported here was performed for the. U.S. Army's

Communications Systems Agency (CSA), Ft. Monmouth, NJ, by the

Institute for Telecommunication Sciences (ITS), Boulder, CO. It

, i s part of a cont tnui ng program in support of that agency' s

Access Area Digital Switching System (AADSS) program on project

orders 501-RD, 804-RD, and 809-RD.

Previous related study reports are as follows:'

IIParametric Cost Alternatives for Local Digital Distribution

System," M. Nesenbergs and R.F. Linfield, OT Report 76-95,

March 1976.

"Preliminary Evaluation of Hub Alternatives for Access

Area Digital, Switching," J.C. Blair, Special unpublished ITS

report to CSA, October 1977.

"Access Area Switching and Signaling: Concepts, Issues,

and Alternatives,1I R.F. Linfield and M. Nesenbergs,

NTIA Report 78-2, August 1978.

"Control Signaling in a Military Switching Environment,1I

R.F. Linfield, NTIA Report 79-13, January 1979.

Administrative and technical monitoring of this current

study contract was performed by Mr. T. Michelli of CSA. Technical

and management supervision of the program at ITS was provided by

Dr. P.M. McManamon.

iii

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

ABSTRACT

1. OBJECTIVE AND SCOPE

2. SWITCHING CONCEPTS AND DEFINITIONS

2.1. Switching·System Classification

2.2. Interfacing and Signaling

2.3. Switch Selection Criteria

2.4. A Digital Circuit Switch and its Call Processing

FUlJctions

3. CHARACTERISTICS OF EXISTING CIRCUIT SWITCHES

4. FACTORS LIMITING CIRCUIT SWITCH CAPACITY

4.1. Traffic Offered to the Interface

4.2. Interface Multiplexing and Concentrating

4.3. Traffic Circulation in the $wi~ching Matrix'

4.4. Interrelationships Between Capacittes of- Switch

Elements

4.5. Capacity Limitations of the Control Element

4.6. Control Signaling Systems· Impact on Capacity

5. TRAFFIC ENGINEERING

5.1. Needs ~nd Background

5.2. The Server Trunks Between a Concentrator and

Its Switch

5.3. Common Facility for Two User Types

5.4. Unresolved Traffic Issues for Switching Networks

6. APPLICATION TO FT. MONMOUTH ACCESS AREA

6.1. Access Area Profile

6.2. Basic Assumptions and Implementation Concepts

6.3. Digital Switching Requirements for Main Post and

Nearby Installations

7. SUMMARY, CONCLUSIONS,AND RECOMMENDATIONS

8. REFERENCES

v

Page

vii

xii

1

1

4

6

17

22

23

28

35

37

41

47

~5,

59

76

82

82

89

94

98

103

113

122

128

138

141
·APPENDIXA. DETAILS OF THE CONCENTRATOR/SWITCH SERVER TRUNK

PROBLEM 145

A.1. Problem Definition 145

A.2. Approximating Model 147

A.3'. The Approximate Solution 150

A.4. Numerical Results 152

A.5. References 159

APPENDIX B. DETAILS OF THE COMMON FACILITY PROBLEM FOR

TWO TYPES OF USERS 161

B.l. Problem and Its Solution 161

B.2. Numerical Results 164

B.3. References 170

APPENDIX. C. THREE KINDS OF CALLS AT A LINE/TRUNK SWITCH 171

C.l. Assumptions 171

C.2. Equilibrium Equations 172

C.. 3. The Formal Solution 174

C.4. References 175

vi
Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11 .

Figure 12.

Figure 13.

Figure 14.

Figure 15.

LIST OF FIGURES

Page

Basic deployment concept of access area switch hubs

and long haul networks. 3

The four basic elements of a telecommunications network

switch. 5

Switch technology classification. °7

Analog switch configurations~ 9

Digital switch configurations. 10

The AN/TTC-39 merged technology switch. 11

Control technologies used in circuit switching systems. 13

Block diagrams of two basic switch types. 16

Interfacing digital and analog terminais with digital

and analog switches. 18

Signaling technologies used in circuit switched

networks. 21

Switching system selection based on traffic classes and

transmission properties. 24

Digital switching system with T-5-T switching matrix. 25

Line occupancy for a number of. call s. 38

Traffic intensity 'per line as a function of call

rate and holding time. 40

Approximate operating ranges for line and

trunk traffic. 42

Figure 16. The effect of the number of sources on capacity

of 10 trunks with 0.01 blocking probability

and assuming blocked calls are cleared. 44

Figure 17. Concentration achievable for one-way blocking

probability of 0.01 and assuming blocked calls

are cl eared. 46

Figure 18. Average traffic circulation per line and per

trunk for a specific example. 48

vii
Figure 19. Traffic circulation in switching matrix as a

function of community of interest. Line ports

fixed at 300 and tr~nk ports added for interswitch traffic.

Figure 20. Traffic circulation in non-blocking matrix with

total number of lines and trunks fixed at 300.

Figure 21. Relating average subscribers call rate to total

call attempts.

Figure 22. Relating total call attempts to number of

terminations.

Figure 23. Relating processor capabilities to matrix

capacity.

Figure 24. Composite of figures 14, 21, 22 and 23 for

switch system capacity evaluation.

Figure 25. Overlay demonstrating capacity of large toll

switch.

Figure 26. Switch sizing relationships.

Figure 27. Capacity estimates of some commercial

switching systems.

Figure 28. Estimating processor capability requirements.

Figure 29. Possible control element architectures for

stored program controlled switches.

Figure 30. Program size for some commercial switches.

Figure 31. Memory requirements versus processor

, capabi 1ity.

Figure 32. Impact of service features on processor

capacity.

Figure 33. Control signaling via common channel

signaling l ink.

Figure 34. Basic format of signal units used with

common channel interoffice signaling system.

Figure 35. Steps required for 10-digit call using eelS.

Figure 36. Common channel signaling traffic intensity

versus signaling rate.

viii

50

51

52

53

54

56

58

60

62

64

67

70

73

75

79

80

81

83
Figure 37. Common channel call attempt capacity.

Figure 38. An outline to probability of blocking estimation.

Figure 39. The server trunks or tie lines between a

concentrator and a switch carrying two

types of calls: distant and local.

Figure 40. Region of uncertainty created by unknown

mix of distant (A) and local (8) call loads.

Figure 41. Estimated total load vs. number of servers

for the assumed practical Po and AlB values.

Figure 42. Examples of m-server facilities for two

user types: (a) concentration of lines and

trunks; (b) sharing of signaling units; and

(c) circuit and packet switching integration.

Figure 43. Two user types, called lines and trunks, share

a common m-server facility with a loss-delay

feature.

Figure 44. The traffic flow model for the loss-delay

hybrid.

Figure 45. Bounds and estimated total load (La+Tb) versus

required number of servers (m) for 1% blocking

probability, parametric in hybrid parameter 8,

and for the indicated values of L, T, a and b.

Figure 46. Three kinds of calls through a switching network.

Figure 47. Hierarchical network configurations for interregional access.

Figure 48. Regional access to the military reservations

in New Jersey area via T-carrier.

Figure 49. Strategic access to digital European backbone

via OSCS.

Figure 50. Ft. Monmouth and its environs.

Figure 51. Ft. Monmouth main post.

Figure 52. Population distribution for Ft. Monmouth.

ix

84

88

90

92

93

95

97

99

100

102

105

106

107

114

115

120
157

156

154

153

Figure 54.

Figure 55.

Figure 56.

Figure 57.

Ffgure 58.

Figure 53. Implementation concept for digital concentration,

multiplexing, switching and trarismission in the

access area. 123

Local and remoted components of a switching hub. 124

Traffic flow assumed for remote switching hubs. 126

Trunking from main post to environs, Ft. Monmouth, NJ. 129

Concentration, switching, and trunking on main 'post,

Ft. Monmouth, NJ. 130

Oigital concentration, switching and trunking

requirements for mainline telephones in

Ft. Monmouth access area. 131

Figure 59. Relationship between switch capacity requirements assuming 3-minuteaverage holding time. 137

Figure A-l. An approximate model for m server trunks

between a concentrator and a switch. 148

Figure A-2. Approximate probability of blocking for distant

calls Po (based on fraction of time) versus the

initial load M(a+b) parametric in distant/local

load ratio a/b, for M=20, m=lO.

Figure .A-3. Approximate probability of blocking for local

calls P

L (based on fraction of time) versus the

initial load M(a+b) parametric in distant/

local load ratio alb, for M=20, m=lO.

Figure A-4. Approximate probabilities of distant call

blocking Po ~nd local call blocking PL (both

based on time) versus the initial load M(a+b),

parametric in a/b, for M=48, m=24.

Figure A-5. The approximate ratio of local and distant call

blocking probabilities, PL/PD, for P

D;lO-2 and

2:1 concentration of lines.

Figure A-6. The approximate distant call blocking probability

Po versus effective total offered load, A+B,

parametric in Mand m, and subject to A/B=1/3. 158

x
Figure B-1. Probability of blocking Pm (based on fraction of

time) versus the initial load, La-Tb ; for

parameter values indicated.

Figure B-2. Bounds on probability of blocking Pm (based on

fraction of time) versus the initial load,

La+Tb, for parameter values indicated.

Figure B-3. Approximation of blocking probability Pm

(based on fraction of time) versus the

initial load, La+Tb, for parameter values

indicated.

FigureB-4. Blocking probability approximations for

various initial loads, La+Tb, versus the number

of servers m. For L=50, T=10 and b=5a.

xi

165

166

168

169
Table 1.

Table 2.

Table 3~

Table 4.

Table 5.

Table 6.

Table 7.

Table 8.

Table 9.

Table 10.

Table 11.

Table 12.

Table 1,3.

Table 14.

Table 15.

Table 16.

Table 17.

Table 18.

Table 19.

Table 20.

Table 21.

Table 22.

Table 23.

LIST OF TABLES

Functions Performed by Various Types of Control Signals

Call Processing Functions Performed by Circuit Switch

Elements

Typical Switch Characteristics for Toll, Tandem and End

Offices

PABX Switch Characteristics

AN/TTC-38 Switching System Characteristics

AN/TTC-39 Switching System Characteristics

Some Factors Limiting the Capacity of Circuit

Switch Elements

Switch Sizing Relationships

Possible Number of Switch Term;-nations When

Control Processor is Limited to 10,000 Busy

Hour Call Attempts

Software Categories

Software Development for No.1 ESS

Selected PABX Service Features

Representative Values of Contributors to

Telephone Network Access Time

Methods of System Characterization

Estimates of Military Communications Terminals,

Local to Wordlwide

Parameters Required for Access Area Planning

Ft. Monmouth Access Area Demographics

Ft. Monmouth Access Area Telephone Environment

Ft. Monmouth Access Area Data Terminal Environment

Number and Types of Terminals Projected for

Ft. Monmouth Access Area in 1985

Terminal Density Profile

Intra-area and Interregional Trunking Facilities

Main Pos~ Remote Switching Hub Capacity Requirements

xii

Page

20

27

29

30

31

33

36

61

65

69

71

74

77

86

109

110

116

117

118

119

121

128

133
Table 24. Main Post Central Switching Hub Line and Trunk

Loading 134

Table 25. Summary Characteristics for Central (Main Post)

and Remote (Squier Hall) Switching Hubs 136

Table C-l. Summary and Notation fQr the Three Kinds of Traffic 171

Table C-2. Occurrence of Local, Distant, and Tandem Call

Blocking as a Function of State Index Set (~,d,t) '172

xiii

SWITCH ELEMENT CAPACITIES IN ACCESS AREA DIGITAL SWITCHING SYSTEMS

R.F. Linfield and M. Nesenbergs*

The capacity of a digital circuit switching system is defined

in terms of its four major elements: the traffic offered by the

interface element, the maximum traffic carried by the switch

matrix, the maximum number of call attempts handled by the

control processor, and the maximum number of calls handled by the signaling elements. These element capacities may be

engineered for the expected traffic (e.g., caJl attempts and

holding times), the performance objectives (e.g., blocking probabilities and tolerable delays), the processor capabilities

(e.g., speeds, memory sizes, service features), and the

signaling techniques (e.g., common channel or per-channel signaling). . In a properly engineered system, the interrelations between

the capacity of all elements should be considered. This report discusses such interrelationships and characterizes representative switch configurations on the basis of the four major elements.

The results obtained have applications in developing non-tactical

networks for military access areas where the communications

profile is known. This is demonstrated for Ft. Monmouth and its

environs. Estimates of traffic statistics and switching requirements are made with the aid of available Ft. Monmouth terminal

density profiles.

1. OBJECTIVE AND SCOPE

The Institute for Telecommunication Sciences (ITS) has been conducting a

series of studies on access area communications for the U.S. Army Communications Systems Agency (CSA). The purpose of these studies is to assist the

Army in its competitive concept evaluations and procurement efforts for

upgrading non-tactical networks in the milftary access areas. This is to be

accomplished by providing CSA, plus other Army or DoD organizations, with

needed information on the state-of-the-art capabilities of switching,

signaling and distribution systems.

Previous efforts conducted by the Institute and reported earlier include

studies of cost alternatives' for local digital distribution systems, pre-

*The authors are with the Institute for Telecommunication Sciences, National

Telecommunications and Information Administration, U.S. Dept. of Commerce,

Boulder, CO 80303.
liminary switch hub evaluations, digital switching concepts, and control

signaling techniques. The study reported here extends the previous work on

switching concepts to include a realistic assessment of switch system capacities. Particular emphasis is placed on the processor capabilities in stored

program controlled (SPC) systems.

Digital switches with stored program control, and especially when augmented with digital transmission facilities, provide new service features and

system functions to the user. It appears that this digital technology can,

at the same time, permit reductions in space, power, and eventually,

operating and maintenance costs.

The application of digital ~echnology to military access area posts,

camps and stations further extends the digitization process from the Defense

Communication System (DCS) long-haul backbone to the local level. This helps

resolve many otherwise complex interface issues.

Figure 1 is a simplified deployment diagram which illustrates how

centralized switching hubs in the access area provide gateways to the DeS

network and to commercial common carrier networks. The central hubs also

provide all required local access area telecommunication services. Remote

hubs, PABX·s, multiplexers, or concentrators located at terminal cluster

points assist the central hub in these services.

This report defines the parameters which determine the capacity of

modern switching systems (Sec. 2). Existing commercial switching systems are

used to exemplify the characteristics of representative switches (Sec. 3).

Numerical parameter values are developed for a range of switch sizes. These

are chosen to have application in the military access area (Sec. 4). Teletraffic engineering concepts are introduced in Section 5. The results are

applied to a specific military complex whose communications profile has been

previously determined (Sec. 6). The concluding paragraphs outline additional

key studies which are necessary to specify the digital switching system for

the access area (Sec. 7).

2
DCS BACKBONE COMMON CARRIER

END

OffiCE

END

OffiCE

REMOTE

HUB

Terminals

MUX/CONC

REMOTE

HUB

ACCESS AREA

MUX/CONC

Figure 1. Basic deployment concept of access area switch hubs- and

long-haul networks.

3
2. 'SWITCHING CONCEPTS AND DEFINITIONS

A switch is a device used to interconnect two or more circuits or to

store~ process, and forward telecommunications traffic. Ina telecommunications network, sWitching permits more economic sharing of transmission

facilities between switching centers and stations on a periodic or demand

basis. Switches are used either to configure the transmission paths through

a network or to provide temporary access to the network on a potential

message delay basis. In the first case, termimals are connected in real

time. They are said to be circuit switched. In the second case, one has

store-and-forward switching. It imposes a prospective penalty of potential

service delays in order to use transmission facilities more efficiently.

The major elements of a network switch are depicted in Figure 2. The

four basic elements and their primary functions are:

1. The interface element, which matches the switch to the. transmission

facilities (l·ines to terminals, trunks to other switches) or to

other.network resources (signaling channels, service circuits).

2. The configuration or access element, which can change its state in

space, time or frequency, depending on control instructions.

3. The control element, which makes decisions and activates changes.

4. The signaling element, for sending and receiving control messages.

Switches can be implemented in numerous ways using a variety of technologies f6r each element. In some configurations, the functions performed

by separate ~lements may overlap. The type of switch selected for a

particular application depends on the nature of traffic it must handle and

the transmission environment in which it must operate.

In the following subsections the technologies available to the four

basic elements are defined. The evolution of switching from manually

controlled switches to electronic switches with stored program control is

reviewed. Criteria for selecting a certain type of switch for a given

application are discussed. Finally, the call processing functions performed

by each element of a circuit switch are summarized.

These introductory concepts and definitions serve as the basis for

characterizing modern, commercially available, circuit switches.

4
To and from

Other Network

Resources

NETWORK

INTERFACE

ELEMENT

CONFIGURATION

OR DELAY.ACCESS

ELEMENT

SIGNALING

ELEMENT

CONTROL

ELEMENT

Figure 2. The four basic elements of a telecommunications

network swi tch..

5
2.1. SWitching System Classification

Telecorrmunication switch systems today fall into two basic classifications -- circuit switches and store-and-forward switches (see,fig. 3).

Circuit switches have been used for switching telephone networks for nearly

one hundred .years. Circuit switches generally involve bidirectional information transfer with essentially no delay. Store-and~forward switches, in

contrast, involve unidirectional information transfer that may be delayed.

An early form of store-and-forward switch was the torn-tape message center.

Today high-speed computers with mass memories perform the message reception,

processing, storage and forwarding functions.

Circuit switches are normally distinguished by the technologies used in

two of the basic elements, the switching matrix and the control.

Store-and-forward switches are typically categorized by the method used

to format the message (e.g., length and header). The format affects the

delay in the network. Distinguishing aspects of both types are discussed in

the following subsections.

.2.1.1. Circuit Switch Technology

The switching matrix in a circuit switch may be either analog or

digital, as indicated in Figure 3. The analog and digital matrices may be

subd1vided further into either space-divided ('SD), time-divided (TO), or

frequency-divided (FD) networks. On~ talks accordingly of space-division,

time division, or frequency division circuit switch technologies. These

switching matrices are 'used to establish a direct connection between communication terminals.

A space-division matrix provides a physical connection between two or

more circuits via a unique series of spatial points, at a given time. Timedivision and frequency-division matrices provide this connection through

equivalent unique points in time or in frequency.

Analog space-division switches have been commonly used in the past.

Today, the trend is toward digital time-division switches. Frequency-.

division switches are rarely used.

In analog circuit switches, information is represented in analog form.

For instance, voice signals may be modulated on carriers. Digital circuit

6
CIRCUIT SWITCH

SWITCH'TECHNOlOGIES

STORE...A8D-'FORWARDSWITCH

---- - --- ---. ------------

HYBRID

ANALOG

'"""---------- .........

FREQUENCY

DIVISION

SPACE

DIVISION

MERGED

TIME

DIVISION

DIGITAL

----

SPACE TIME

DIVISION DIVISION ............ .......- .......................... ......-......-

COMBINATIONS

DATAGRAM

SERVICE

PACKET

VIRTUAL

SERVICE

MESSAGE

TERMJNAL

EMULATOR

METALLIC SEMICONDUCTOR

CROSS POINT CROSS POINT

Figur~ 3. Switch technology classification.
switches route information in digital form. When digital switches are used

in telephony, some form of vofce digitization process (VDP) is -required.'

Analog voice signals are sampled and converted to binary words. Various

means of conversion are used, the most common being pulse code modulation

(PCM). Subject to memory compatibilities, the binary words from many sources

are interlaced serially onto a common highway or bus with the aid of a timedtvtsf onmul t tplexer (TDM) or a concentrator. Switching Is accomplished by

interchanging the ~ime slots on the bus. This time slot interchanging (TSI)

process may be combined with a space-divided network. The advantage of a

joint spatial and time gating techniqu.e between buses is to provide parallel

sets of avai lable time sIots, There are many possible combinations of time

a~d space division switching stages.. Examples of some, analog and digital

switch configurations are sh6wn ~n Figures 4 and 5.

c In g_eneral ,the analog switches u'se linear crosspoints in the matrix.

An exception~ccurs when an an~log signal is converted to pulse width or

pulse time modulation. No confusion results if these are still considered

analog switches.

The digital switch configurations shown in Figure 5 e~ploy non-linear

circuit elements." Binary bit streams could, of course, be'swit~he9 by a

linear crosspoint. However, conventional ana]og signals and pulse amplitude

modulated signals cannot be switched using non-linear devices.' .

It is feasible to combine analog and digital technologies in a single

switch. An example of such merged technology switch is the tactical switch

being developed by the Joint Tactical Program Office known as'TRI-TAQ. This

switch, designated the AN/TTC-39, uses electronic crosspoints in a spacedivided matrix to handle analog terminations, and a time-divided matrix to

handle digital termf nat i ons. Continuously variable slope delta (CVSD) .

modulation is used for the VDP between the. two matrices. A simplified block

diagram of the AN/TTC-39 merged technology switch is shown in Figure 6.

One aspect of switch classification which is not included in Figure 3 is

the coexistence of two-wire and four-wire switching. A telephone connection

can carry voice signals in both directions simultaneously over one pair of

wires. This is normal practice between a telephone and a circuit switch.

Switching is often, but not always, accomplished by using bidirectional

8
Analog

Lines

a

Trunks

Analog

Lines

8

Trunks

Digital

Lines

a

Trunks

- - Analog

- - L1NEAR

- - INTERFACE - - SPACE DIVIDED -- - -... ,

-- - MATRIX -- .,,-

J~ -J~

,i 'v

, .

SIGNALING -... - CONTROL -

- - PAM LINEAR Ii -... .,- PAM - - & -- - TIME DIVIDED - ,- --- ,.

-..- .,- - MUX/CONC MATRIX

J~ J~

,~ ,~

SIGNALING .- CONTROL

- - - - Analog LINEAR D/A,A/D - - - - -- TIME &SPACE .,,-

MUX/CONC -- .,

--.

- ",,-

- DIVIDED MATRIX

J~ j~

,~ ,~

SIGNALING -- - CONTROL - ----

Figure 4. Analog switch configurations.

9
Analog

Lines

8

Trunks

Digital

Lines

a

Trunks

.-

--.. -- NON-LINEAR VDP Digital - - - "'- .............. --- . - - TIME DIVIDED NUX/CONC - ...... ---.. MATRIX - J~ J~

'V 'v

SIGNALING - ...... -.... CONTROL ---

- - Digital NON-LINEAR - - ...... NUX/CONC .- .........

- - - - T.IME DIVIDED -'-

--....- -

- MATRIX

J~ J~ .

'V 'V

SIGNALING - .........

- CONTROL --

Figure 5. Digital switch configurations.

10
Analog

Lines

a

Trunks

Digital

Lines

a

Trunks

ANALOG

SWITCHING

MATRIX

INTERMATRIX

COOEC

DIGITAL

SWITCHING

NATR1X

STORED

PROGRAM

CONTROL

Figure 6. The AN/TTC-39 merged technology switch.

11
crosspoints. Cost and return-loss considerations affect the crosspoint

selection. In an analog carrier system using frequency-division multiplexing

(FDM) and digital carrier using time-division multiplexing (TOM), however,

the two directions of transmission must be separated because amplifiers,

modulators, codecs, etc., arerinher-ently unidirectional devices. Thus within

the matrix, each direction of transmission and the switching requires two

pairs of wires. Thj5four-wire transmission and switching loop can be extended

to the subscribers Ltermtna ls for digital voice and data transmission. There

are possibilities of easier encryption. The four-wire switching matrix has

the advantage of infinite return loss. It mtn imizes echo and singi.ng

problems at the switching point. Digital switches considered in this report

are assumed to perform four-wire switching. "Four-wire" operation implies

full duplex operation with separate time-slots in the time~divided networks.

2.1.2. Control Technology

There are a variety of techniques used to control a circuit switch. The

techniques depend on the functions to be performed and the matrix configura-

- tion. Figure 7 shows the various control technol oq ies employed by circuit

switching systems .and the approximate year each technology was introduced.

Early circuit switches were analog in nature and used space-division

matrices to interconnect transmission facilities. These switches started

with manually controlled switchboards that used plugs and jacks. They

evolved into electromechanical step-by-step switches with direct control,

. panel switches with indirect control, and crossbar switches with common

relay-type control. Gas tubes and magnetic-reed relays were also used for

crosspoints. In the late 1950 1

s , electronic switches were introduced.

Electronic gates were implemented mostly with semiconductor devices. They

replaced not only the metallic crosspoints of the space-divided matrix, but

also the wired circuitry of the common control logic. As switching systems

increased in size and new service features and system functions were added,

many of these wired logic control funct10ns were replaced with software

routines stored in the memory of a central processor.

Large scale integrated circuit developments have made it practical to

use wired or permanently stored program logic which resides in read-only

memories (ROM). This so-called firmware cannot be changed easily. It also

12
MANUAL

(1880)

ELECTRO-MECHANICAL

(1920)

CONTROL TECHNOLOGY

ELECTRONIC

('1950)

DIGITAL

(1970)

--'

w

DIRECT INDIRECT COMMON

FULLY

WIRED

(DISTRIBUTE D)

PARTI"ALLY WIRED

(ACTION

TRANSLATOR)

SINGLE MULTI

PROCESSOR PROCESSOR .

~.

COMMON DISTRIBUTED

STORE STORE

Figure 7. Control technologies used in ~ircuit switching systems.
does not require continuous power. Sometimes the entire control logic may be

wired program logic (WPL) in this form. This class of control is known as a

distributed logic system. Other systems may use combinations of wired

program logic and stored program control (SPC) logic which is in the form of

software. Software may be electronically stored in random or structured

access memories (RAM). The contents of RAMls are easily changed. Usually,

programs are loaded into the RAM from an external magnetic tape or disk.

This type of software requires reloading after power failures. An example of

this type of WPL and SPC system is the action translator. In the trade, the

term action translator is synonymous with stored program translator. It

refers to memory devices that perform a specialized table look-up function.

That function serves to control only the sequence of call actions (Joel,

1977).

Stored program controlled systems' employ a variety of system archi-

.,." 'tectures. The RAM may be associated with a single processor, with multiproc~sso~s or several processors~

. A more d~tailed discussion of the evolution of circuit switches and

the ir icontr-o l is given by Joel '(1977) and Leaky (1977).

2.1.3. Store-and-Forward Switches

Unlike circuit switches, stor~-and-forward swftches do not require a

switcning matrix for establishing a connection. Instead, the information

(e.g., digital data) to be transferred is stored in a memory devfce until the

network is ready for transmission. There are two basic types of store-andforward switches -- message and packet (see Fig. 3). Message switches are

designed to handle blocks of digital data. The block size may be variable

within some maximum bound. Each block is usually headed by its own destination address. The message switch stores the first block. The block is

forwarded towards the destination address when a suitable transmission

facility becomes available. Thus, the message block can be delayed by

varying amounts that depend on the available channels and their topology.

Delay times often range from minutes to hours. The sto~age facilities are

used in lieu of more costly transmission facilities.

Store-and-forward packet switches are similar to message switches

"except each individually addressed block is limited to short sequences of

14
information bits called packets. The packet size is usually fixed. A

typical length is of the 'order of·1000 bits. The packet consists of information bits and the header which contains source, destination, type, priority

and other transmission information. No long-term storage is required in'a

packet switch. Packets are held only for short periods and are sent individ-:

ually tbward their ~estination as rapidly as possible. Alternate routes may

be used for individual packets in a sequence of packets. Delay times vary

due to the alternate routing but are typically less than one hundred milli-

. seconds. Packets may be lost in transit or ~ven discarded if storage facilities are exceeded. In these cases, ~etransmission is normally requested.

Store-and-forward switches .may process digital data which resides in

storage or as ,it flows through the switch. Co~munication processing functions

include code and speed conversion', that make the switch compatible with a

variety of terminals. Processing may also include other functions, such as

error detection and correction, which assist in the transmission of information. The amount of processing provided depends to some extent on the users·

requirements and the user interface. Three types of interfaces have been

defined by Roberts (1977) for packet switched networks. They are: the-'

datagram interface, the virt~al circuit interface, and the terminal emulation

interface.

In many instances, the user can select the interface of his choice. The

service features provided to the user by these interfaces are functions of

the amount of processing provided. The datagram interface requires the least

amount of processing. Datagram terminals, not the interface, are responsible

for detecting duplicate and lost packets, for requesting retransmissions, for

sequencing packets, and for overall flow control through the network. With

virtual circuit terminals, the switch interface provides most of these functions. However, some functions, such as flow control, are still the responsibility of the host computer or its front end processor. In the terminal

emulation interface, all of the functions are the responsibility of the

p~cket switching network. Almost any type of host computer is therefore

directly compatible with any communications process.

The basic building blocks of a circuit switch and a store-and-forward

switch are compared in Figure 8. The control logic for both switches~is a

15
A. Circuit Switch

SWITCHING

MATRIX

To and from

Terminals

a

Other Switches

CONTROL

PROCESSOR

SIGNALING

EQUIPMENT

STORED

PROGRAM

B. store-end- forward Swi tch

MASS

STORAGE

To and from

Terminals

a

Other Switches

ACCESS

INTERfACE

CONTROL

PROCESSOR

STORED

PROGRAM

Figure 8. Block diagrams of two basic switch types.

16
stored program in the memory of a digital computer or processor. The circuit

switch employs a time or space divided switching matrix whereas the storeand-forward switch, employs mass storage facilities to hold information prior

to forwarding. The control _sign~ling information is included as overhead on

each message or packet and is not shown as a separate element in Figure 8.

2.2. Interfacing and Signaling

In the previous section, it was shown how switches may be classified in

terms of the t~chnology used for the switching matrix and the control. In

additiotJ, the switch may be siz~d in terms of the number of ports or termi~at ions tt.presents to the outside world. The interface between the switching,

matrix and" the transmission facilities determine this size. In. a digital

circuit switch, the interface may be the principal element which determines

the probability that a connection is blocked; i.e., the grade of service.

These aspects of the interfa.ce are discussed in Section 4 and in Section 5.

In any given telecommunications network, the user terminals and the

transmission facilities, as well as the switch, may be analog or digital.

The interface at a given type of switch must provide the match to the transmission environment in which the switch operates. Figure 9 illustrates

various combinations employed to interface a given analog or digital terminal

to its particular local, either analog or digital switch, via analog or

digital transmission facilities. 'All the paths between terminals and switches

are considered bidirectional in Figure 9; i.e., terminal-to~switch follows

same path back to terminal~

Caution -- to avoid misunderstanding, Fig~re 9 is to be interpreted

literally, and in the following specific way only. The figure applies ~o a

given unique terminal and its equally unique switch. Thus, if the terminal

in question is analog and the end office switch is also analog, one uses the

upper left part, (a), of Figure 9. There are two ways for this terminal to

interface with its switch, namely, vi'a analog or digital transmissions.

Either one or the other, but not both, paths are permitted in the figure.

Tracing of loops is thus not to be done in Figure 9.

If the analog terminal is served by a digital switch, the same two

transmission options exist, provided that CODEC's are located at the appropriate ends of the path.

17
(a)

ANALOG

TRANSMISSION

ANALOG

SWITCH

. ANALOG

TERMINAL

DIGITAL

SWITCH

(b)

DIGITAL

TERMINALS

DIGITAL

TRANSMISSION

ANALOG DIGITAL

SWITCH SWITCH

Figure 9. Interfacing digital and analog terminals with digital and

analog switches.

18
If the terminal in question is digital, one tu~ns to part (b) of the

figure. Depending on the nature of the switch, either analog or digital,

there are only two ways of placing the MODEM's to suit the two options for

transmission facilities.

Analog signals must be AID converted (coded) to be transmitted or

switched in digital form. Likewiset they must be DIA converted (dec9ded)

upon reception. This coding-decoding process is performed by the codecs

shown in Figure 9(a).

Digital signals may modulate carriers to be transmitted or switched in

analog (sometimes alluded to as quasi-analog) form and demodulated when

received. This modulation-demodulation process is performed by the modems

shown in Figure 9(b).

A given switch can operate in a dual environment using appropriate

modems and codecs at the interface. A digital circuit switch with separate

interfaces for digital and ,analog lines or trunks is described in Section 2.4.

The-interface matches'the transmission facilities to the switching

element. It also prov~des the means for remoting the control element by

means-of the signaling element.

Signaling in telephony involves the exchange of electrical information

(other than speech) which' is specifically concerned with establishing,

maintaining, and disengaging the connections. Signaling is also ~sed to

manage the network, to control the floW of traffic, monitor status and

. assess performance. Signaling systems provide the control tnformation

required to operate switches and terminals, ensu~e efficient and reliable

transmission, and overall network administration. Table 1 lists several

basic functions performed by the' control signaling sy~tem.

The signaling -required to remotely control a circuit switch is sometimes

related to the interface. This occurs when user information and control

information share the same transmission channel. When separate channels are

dedicated for signaling, a separate'interface is required. Signals may be

transferred between terminals and switches (station signaling) and between

switching points (interswitch signaling) using different technologies and

modes of operation. Figure 10 provides a br~akdown of the major signaling

technologies used in circuit switched networks.

19
Table 1. Functions Perfdimed by Various Types of Control Signals

Terminal Control Signals

o Attending

o Addressing

o Alerting

o Supervision

Switch Control Signals

o Registration

o Translation

o Path Searthing and Selection

o Routing

Transmission Control Signa'ls

o Synchronizing

o Error Detecting

o Testing

Network Management

o Flow Control

o Status Monitoring

o Performance Assessment

o Reconfiguring

0, Recordi ng

20
SIGNALING TECHNOLOGY

ANALOG TRANSMISSION

----------- QUASI-ANALOG

TRANSMISSION

DIGITAL lRANSM1SSl0N'

N

......

PER CHANNEL COMMON CHANNEL 80RROWED'8~ITS ALLOCATED BITS

DC PULSE AC PULSE ASSOCIATED NO·NASSOCIATfD ASSOCIATED . NQNASSOCIATED

IN B'AND OUT-OF--8AND QUASIASSOCIAT·ED

FULLY

-DISASSOCIATED.

SINGLE

FREQUENCY

MUlTIFREQUENCY

Figure 10. Signaling technologies used in circuit switched networks.
The control information inputs to the control element are, in most

cases, generated by a process known as scanning. Outputs from the control

element are dispersed by the distribution process. Distribution and scanning

may be performed at the interface where' signaling is accomplished on a perchannel basis. For common channel signaling and in store-and-forward switched

networks, these functions are performed by the control processor itself.

Control signaling in a military switching environment is described in

detail by Linfield (1979).

2.3. Switch Selection Criteria

The criteria for selecting the switch type for any given application is

largely dependent on the nature of user terminals and their traffic demands.

Terminals may have wide disparities in traffic rates, transaction sizes,

delivery times and specific performance, such as synchronization, requirements.

The transmission rates may vary from 100 bits per second for teletypewriters

to megabits per second for wideband video and graphics. Transaction sizes

range from less, than 10 bits for character-oriented interactive codes to

several megabits for bulk data transfers. Delivery time characteristics vary

from continuous real time to intermittent data. Acceptable delays could be

on the order of milliseconds, or minutes to hours for interruptable bulk

data.

Different switch technologies may fit different kinds of traffic. The

circuit switch is inhe~ently a 2-way transparent switch and is ideal for

handling continuous traffic with long holding times, such as on the order of

one minute or longer. Circuit switches provide real-time connections between

-compatible terminals such as the telephone. Blocking due to congestion in

the switch, or elsewhere, may occur.

The message switch is inherently one-way and is essentially nonblocklnq . Relatively long delivery delays may be encountered. Message

switches are therefore suitable for handling terminals that generate interruptable types of traffic, such as facsim;-le or teletype. Terminals need not

be compatible, since code, mode and speed conversion can be accomplished at

the switch. The packet switch. is well suited to handle interactive traffic

that comes in short bursts. Such data flow is generated by the query and

response interactions between host·computers and their terminals.

22
Figure 11 summarizes the traffic types and, the switch applications in

terms of desirable network properties (Kleinrock, 1976a). The three sides of

the tri angle in thi s fi gure represen-t a network property whi-ch the user

desires. These desirable properties are high reliability, large throughput

and short delay.

At each apex of the triangle, any two desired properties can be achieved

by neglecting (and in most cases, counteracting) the third property. Thus

continuous real-time traffi~ in the lower right corner requires large throughput with low delay, but does not typically require high reliability. This is

the situation for digital voice networks and can be handled by a circuit

switc~. Interruptable traffic, such as file transfer, appears at the peak of

the triangle. This requires large throughput and high reliability, but can

be delivered with long delay. The message switch 15 suited for handling this

interruptable traffic.

It may, in the future, be feasible to combine the functions of all three

types of ,switches into a hybrid switch capable of adapting to the different

kinds of traffic. One such appr~ach is described by Ross and his colleagues

(1977), whereby circuit and packet switching are combined to integrate voice

and data networks. A packetized virtual circuit for integrating voice and

data o'n a packet switched network is also described by Forgie and Nemeth

(1977). Usually, these integrated approaches sacrifice certain desirable

properties for som~ classes of traffic. Gitman et ale (1977) discuss some of

the issues involved in hybrid s~itching.

In the remainder of this report,' emphasis is placed on digital circuit

switches with stored program ·control. Functions performed by each basic

element of the digital circuit switch are defined in the next subsections.

2.4. A Digital Circuit Switch and its Call Processing functions

The basic elements of a digital circuit switch are shown by the block

diagram in Figure 12. A detailed discussion of this switch configuration is

given by Linfield and Nesenbergs (1978). The line/trunk interface provides

the terminations for subscribers loops from station apparatus and for trunking

to other switches. Anal oq terminations are converted to digital signals by

23
Messa.ge Switch

for

InterruptableTra{fic

Packet Switch:'

for

Interactive Traffic

SHORT DELAY

Circuit Switch

for

Continuous Real'-Time

Traffic

Figure 11. SWitching system selection based on traffic classes and

transmission properties.

24
..

Digital Space I

Switch I

I

I

I

I

I

I

I

I

I

i

I

I

I

I

I ___J

•

TIME

SWITCH

Switching Matrix

,-------.----,

•

TOM

•

Line/Trunk Interface

r--------~--,

I

I

I

I

I

I

Digital

Lines

a

Trunks

Analog

Lines

a

Trunks

·1

L--.I

- - 1. J

,--- -- --:~ ,--- --'~---I

: I SIGNAL I I·· I

I DISTRIBUTION I PROCESSOR I

Common I &SCANNING I I I

Channel -E - -:?-I I I I

Signaling I I I I

II ADDRESS TONE ~~~~I SPC I

REGISTRATION GENERATOR I I ' 'I

I' I L L

. Signaling Equipment Central Control Unit

Fjgure12:. Digital switching" syst,em.withT~,S-T swftchtnq matrix.

25
A/D and O/A converters (codecs). Multiplexing or concentration may also

occur at this point. The line interface also provides ~attery feed, Qvervoltage protection, ~ing access·, ~upervision, £locking or codee functions,

2-wire to 4-wire bYbrid connections, and lest access, otherwise known as

BORSCHT.

Interfaces for both analog and digital lines and trunks are shown in the

figure. It is ap~arent from this figure that remoting the interface is quite

feasible. Furthermore, the analog-to-digital conversion could be incorporated

into the station apparatus with the multiplexer/ concentrator either remoted

or colocated with the switch. Digital Secure Voice Terminals (DSVT) are

feasible by adding encryption and decryption equipment to each terminal.

The interface also provides access for control signaling to the transmi~sion facilities when signaling is provided on a per-channel basis. Such a

signaling technique is assumed in the diagrammed system. Common channel

interswitch signaling is also used. This would be indicated by a separate

interface to a dedicated signaling channel. In Figure 12 the common signaling

channel is shown as a dotted line.

Signaling equipment sends and receives information for controling the

switch from remote terminals or from other switching points. This includes

supervisory signals which indicate line and trunk status, address information,

call progress~tonei, network management, and maintenance or administrative

information.

The control unit interprets the signaling information, makes decisions,

selects paths, and makes the connection via the switching matrix. The matrix

shown in Figure 12 is a time-space-time matrix consisting of short memory

devices to perform time slot interchanges and digital logic gates to interconnect the time-divided highways.

The call processing functions performed by major elements of the circuit

switch are summarized in Table 2. For each element, the pertinent functions

are divided into three categories as follows.

Per-line functions: required on a continuous basis.

Per-call functions: required only during the information transfer

time.

Per-setup functions: required only during access and disengagement

times.

26
N

.........

Table 2. Call Processing Functions Performed by Circuit Switch Elements

Signaling Control Unit Switching Matrix Interface

V)

v);::,

QJeo Attending Input Scanning Battery Feed s:::o::s e,.. e,.. e .(Service Request Overload ....J -iJ e,..

IU-iJ Detection) Protection

QJ::SO s-ee Hybrid o, I.J- U

........,

V) Supervising Interconnection Codec r-- s::: r-- 0 (Call Completion Supervision (tje,..

U -iJ Detection) (Answer and

IU

s-s::: clear)

0) ::s c, I.JV)

e

0 Addressing Registration Establish Connection Ring Access

e,..

-iJ (Sending and Translation Release Connection Test Access

U

e Receiving) Output Distribution ::s

I.J- Alerting Path Selecting

c. (Dial Tone, Routing ::s

-iJ Ringing, Busy Busy Test QJ

U") etc. ) Establish Connection I

s; Release Connection

O)

c,
Admi ni strCltjV~,~ngmaint,~JlgnGe.tYPJ~_s>.Qf, overhead funct.ionswhi ch are not

on-line traffic related, but which are performed by the processor when nb

calls are being processed, are not included in the table.

It is apparent ~hat the control unit is required for call processing

primarily durinqrthe initial call setup and' subsequent disengagement conditions.

One exception to this rule is the' signal scanning process, whi-ch runs continuously, whenever per-line and per-trunk signaJing~quipment.:js used.

.3. CHARACTERISTICSnF EXISTING CIRCUIT,SWITCHES

Summary tabul ati ons of the characteristl cs of some .comnerct a1 type

switches are given in Tables 3 and 41. Specific values for many switches can

be found in the literature or obtained from switch manufacturers. A review

of several switching products is given by Pitroda (1977).

Toll, tandem and end office switch characteristics are summarized in

Table 3. These exemplify only a few of the large range of sizes available in

this category. More recently several switches have been developed which

serve dual roles, e.g., toll and tandem or tandem and end office.

The PABX characteristics in Table 4 represent only a few of the kinds

and sizes available today. Some switches are modula~ in design and one basic

switch.~an be used to meet several sizing requirements.

The characteristics for two military type switches are tabulated in more

deta i 1 in Tab1es 5 and 6. The TTC-38 is an exampl e of .tacti ca1 swi tchi ng

equipment being fielded today. The TTC-39 is a digital and analog circuit

switch which, like the TTC-38, is a shelter-housed, tacti·cal, automatic

telephone control office. This switch is being developed for use in the

early 1980·s. Both~switches are designed to meet the requirements for survivabi 1ity, mob t li ty, and other mi 1i taryenv ironmental (factors.

Some items in Tables 5 and 6 are left blank due to lack of information.

In subsequent sections, we indicate how the various switch parameters

are related. Given ~ertain switch characteristics others can be obtained

from these relationships.

lThe values given ill these tables are representative of typical switches

found in a given.si ze range. The nominal va1ues:forcapaci ty are composi tes

of sevetal switches of similar siz~.

28
Table 3. Typical Switch Charecteristics for·Toll, Tandem and End Offices

SPC SPC SPC

Centralized Centralized Centralized

SOaK 350K lOOK

Custom Custom Custom

26 32 44

500K 250K

Interface

Terminations

AID

Switching Matrix

Technology

Cross Points

N I Carried Load (E) c.o

Signaling

Lines

Trunks

Control

~echnology

Architecture

Capac ity.( SHeA)

Processor

I Word Length (Bits)

Storage (Bytes)

*T = Trun,ks

**L = Lines

Very Large To 11

lOOK T*·

64 kb/s PCM

Digital

Time and Space

50K

Common .channel (CC)

Large Tandem

60K -T

64 kb/sPCM

Digital

Time' and Space

15K

CC

Large End Office

65KL**-

64 kb/sPCM

Analog

Time and Space

5K

DC pulse, DTMF

MF or CC

Small End Office

·15GO···· L

64.'kb/s PCM

'Digital

Ttme

400

DC pulse, DTMF

MF or CC

SPC

Centralized

10K

Microprocessor

16
Table 4. PABX Switch Characteristics

Swi tch II Very La rge

Element

Large Medium Small

Word Lenqth '117 bits

Storage (Bytes) 200K

Control.

Technology SPC

Architecture ·-Centralized

Capacity (BHCA) 25K

Interface

Terminations

A/D

Switching Matrix

Technology

Cross Points

I Load (Erlangs)

Signaling

Lines

Trunks

Processor

7500 (L+T)

64 kb/s PCM

Digital

Time-Space

5K

DC Pulse" DTMF

MF

Custom'mini

2400 L, 600 T

64 kb/s PCM

Digital

Time

1500

DC Pulse, DTMF

MF

SPC

Decentralized

18K

Microprocessors

10 bits

340K

1000 L, 250 T

64 kb/s PCM

Digital

Time-Space-Time

250

DC Pulse, DTMF

MF

SPC

Decentra ltzed

9K

Microprocessor

8 bits

500K

130 L, 30 T

64 kb/s PCM

Digital

Time

45

DC Pulse, DTMF

MF

SPC

Decentralized

1.5K

Microprocessor

10 bits

140K
Table 5. AN[TTC-38 Switching System Characteristics

General

Model

Introduced

Application

Interface

Min. Terminations

Max. Terminations

Load/Line (Erlangs)

Adapter

Multiplexer/Concentrator:

AN/TTC-38

1975

Tandem/End offi ce (Tactical)

320

640

2- or 4-wire

Signaling

Lines

Trunks

Switch/Matrix

Technology

Crosspoints

Carried Load (Erlangs)

Control

Technology

Architecture

Max. Capacity (SHCA)

SF/DC supervision, DC pulse or DTMFaddressing

.: SF/DC supervision, DC pulse or DTMF addressing

Analog space division, 4 stage

PNPN diodes (see note 1)

180

SPC

Central

2700 (600 lines)

31
Table 5 (cant..')

47K

paper tape

Remot~ page printer

GTE Custom (Se.e note 2)

12.5 MHz

5.6

5.6

Ferrite Core

65K (48Kimplemented)

ProcessorCs)

Number and Type

Number of Registers

Word Length (Bits) 24

Instruction Length. (Bits): 24+1 parity

Data Bus (Bits)

Address Bus (Bits)

Clock Rate (MHz)

Cycle Time (l1S)

Access Tfme (lls)

Storage

a Semipermanent

o Permanent

o Off-line

Instruction Set

Call Processing Inst.

Maint. &Adm. Inst.

Peri pherals

Notes

1. Crosspoints 12 channel qroups level FDM, 4-wire wideband (80kHz

channel) information.

2. A second processor/memory unitprovid.es backup. Transfer interrupt

period is approximately 100 ms.

32
Table 6. AN/TTC-39 Switching System Characteristics

General

Model

Introduced

Application

AN/TTC-39

1982 (tentative)

Tandem(End Offi~e

150

660 (with specified mix of analog and digital

switches)

;: . 0.30

CVSD @16 pr~32kb/s

Load/Line (Erlangs)

Digitizer

Multiplexer/Concentrator:

Interface

Min. Terminations

Max. Terminations

Signaling

Lines

Trunks

DC pulse or TITMFaddressing plus others

SF/DC supervision, MF addressing plus others

Switch/Matrix

Technology

Crosspo ints

Carried Load (Erlangs)

Digital and analog

Time'divfde'd and space divided

181 (600 lines)

Control

Technology

Architecture

Max. Capacity (SHeA)

SPC

Centralized

3300 (6,00 1i nes)

33
Processor(s)

Number and Type

Number of Registers

Word Length (Bits)

Instruction Length (Bits):

Data Bus (Bits)

Address Bus (Bits)

Clock Rate (MHz)

Cycl e Time (us)

Access Time (us)

Storage' (words)

o Semipermanent

o Permanent

o Off-line

Instruction Set

Call Processing Inst.

Maint. &Adm. Inst.

Peripherals

Notes

Tabl e 6 (contv )

Litton L3050

Optional

32

32

32

32 (15 used)'

16

100

2.5 (core memory)

Core 3M (typical), 131K (min.)

Yes

Yes

Magnetic tape

100

195K

30K

TTY keyboard, CRT, mag. tape

34
Service features, special system functions, physical charectertst ics,

cost, and performance data are not included in the tables. There are simply,

so many options available that listing them is prohibitive. Also, some of

these characteristics either do not affect the system capacity or are only

indirectly related. Those service features and system functions that do

affect capacity are discussed in Section 4.

4. FACTORS LIMITING CIRCUIT SWITCH CAPACITY

No single parameter has been found .adequate to define the total capacity

of a switch. Individual capacities must be defined for indiyidual switch

elements. The maximum capacity of a given switch may well vary, depending on

the environment in which it is operated.

Table 7 lists the major factors which affect the switch parameters. It

is assumed for this table that the circuit switching matrix is controlled by

a processor with a stored program. The matrix and the interface may both be

analog or digital, and each be blocking or non-blocking. Station signaling

(i.e., control signaling to and from a subscriber terminal) may be in-band or

on a separate channel. Trunk signaling may be on a common channel or pertrunk basis.

The capacity of each switch element may be viewed in different ways

depending on the element1s function. Thus the termination capacity (number

of lines and trunks) is interface and concentrator related. The call attempts

capacity is control and signaling related. The load or traffic intensity

capacity is concentrator and switching matrix orelated. Storage buffers and

routing plans also affect capacity. Inadequacy of any element can limit the

capacity of the total system. The ultimate capacity of the system is also

related to performance. The technology and architecture used in an element,

as well as between elements, may limit the speed of service due to intolerable

delays or they may limit the grade of service due to blocking. A balance

between time-shared equipment from a common pool and the per-line equipment

requires knowledge about the traffic offered, traffic carried, and performance

desired.

For example, the control processor must spend a certain amount of time

on each call attempt. It also must perf~rm certain administrative and main35
Table 7. Some Factors Limiting the Capacity of Circuit Switch Elements

Interface -Element

Access Ports Concentrator

Switching

Matrix

Element

Common

Control

Element

Control

Signaling

Element

Parameter

Defining

Capacity

Units

Terminations; ,Traffic Load

Carried

Number ofLi noes I Erl angs

and Trunks

Traffic Load

Carried

Erlangs

Arrival Rate

Attempts/Hour

Arrival Rate

Attempts/Hour

w

en

Syst~m

Factors

Factors

Determining

Maximum

Capacity

Performance

Limiting

Factors

Area Served

Subscriber

Density

Calling Habits

Features and

Functions

Offered

Probability of

Blocking

~:t\ccess Time

Disconnect Time

Traffic Offered

Cpncentration

Ratio

Ratio of Local

to Distant

Traffic

Number of

Multidrop Lines

Probability of

Blocking

Architecture

Availability

Ratio of Line to

Trunk T-raffic

Holding Time

Constraints

Probability of

Blocking

Architecture

Call Type Mix

Program

Structure

Flow Controls

Speed of Logic

Memory Size

Access Time

Peaking Margin

Service Features

Acceptable

Average Delay

(If Blocked)

Technique. Format

Operating Mode

Signaling Rate

Message Length

Acceptable

Average Delay

(If Blocked)

Error Rate
tenance functions which are not traffic related. As the number of connection

attempts increases, the processor may become fully occupied. Additio~al

. calls then face connection delays that may or may not increase beyond acceptable limits. The processors' real-time capabilities thus limit the system

capacity. This control capacity could be increased by: increasing logi.c

speed, lowering memory access time or by even reorganizing the sortware

access structure.

Certain processing functions could be reassigned by changing the control

architecture or by adding parallel equipments.

In the following subsections the switching element impacts on total

system capacity are discussed.

4.1. Traffic Offered to 'the Interface

The proper design of a circuit switch requires knowledge of thee,xpected

traffic which the switch must handle. This traffic is characterized by the

call arrival rate and the holding time statistics for the offered load,as

well as the corresponding served call statistics for the actual carried load.

For a line that terminates at an interface, the incoming calls tend to

occur randomly and vary in length. The arrival rate (A) per unit time may be

specified as the average number of busy hour call attempts {BHCA)2. The

holding time (T) is the average call duration.

These averaged parameters, A and T,determine the traffic intensity.

Traffic intensity or offered load is the amount of traffic in a path or group

of paths per unit time. It is higher than the actual carried load. The

traffic carried over a single subscribers line is indicated in Figure 13.

For long ave~aging periods, T, the unexpired~allsoccurring at the beginning

and end of the averaging time have a negligible effect. Then the foll,owing

definitions apply.

Average holding time, T = tl+t2+t3+t4+···tn

n

2The BHCA is often determined by averaging busy hours of traffic data from

20 days during a busy season. Day-to-day and hourly variations may be

accounted for by adding a safety margin to the systems' capacity.

37
.

(/)

.....

.....

C't'

•

U

•

0

• s,

QJ

.cE

::3

s:::

C't'

s, 0

>,

-L

u

s:::

C't'

C.

::3UU0

OJ

s:::

.....

...J.M

.....

QJ

s,

::3

CO)

.....

I.J..

38
Average attempt per unit time A'- nIT

These are for the load carried by the lines and offered·to the switch. The

international unit of traffic intensity3 1S the Erlang (E), a dimensionless

quantity. One Erlang of traffic intensity on one line implies a continuous

occupancy of that line. Therefore,

lE =1 call hour/hour =1 call sec/sec.

In North America, traffic intensity is\Jsually expressed in terms of

hundred call seconds per hour and, abbreviated as ccs, with the per 'hour

implied and not stated. Erlangs and ccs (per hour) are related as follows

lE = 36 ccs.

The traffic intensity offered per line as a function of call attempts

per hour and holding time per call is illustrated by the lines in Figure 14.

The maximum intensity carried by any line cannot exceed one Erlang.

The actual traffic intensity is a funct-ion of the subscribers calling

habits. These habits may range from a few calls per day to several per hour.

Holding times may range from less than a minute to an hour or, in rare

instances, more than an hour. Variations in subscriber calling habits also

occur. These variations depend on time of day, day of the week, season of

the year, subscriber location (business versus residential), and other factors.

In summary, the traffic intensity may vary from 0.01 Erlanqs/Ltne for residential subscribers to greater than 0.5 Erlangsl line for some business

subscribers. Trunk traffic may approathfu11 occupancy at times.

The average busy hour load for a subscr-iberIS 1i ne is typi cally about

0.1 E or 3.6 ccs. From Figure 14 this 0.1 E is found to correspond toone 6-

minute call per hour, two 3-minute calls per hour, or six l-minute calls per

hour.

3The terms "traffic intensity" and "traffic load" are used interchangeably

in this report and mean the ~uantity of traffic in one or more paths per

unit of time.

39
10 h

5

5h

2

lh 2h

0.5

0.5 h

0.2

12m

0.1

3m 8m

~.005 0.01 0.02 0.05

3.6s 7.28 18s 36s 72s

2

5

o~.,,("

~"."1.. I".

,... e.~ ')I . " 1\:7 () to k "I': '?g".I

JO

to",

<,,~(!)

20

50

0.5

0.2

0.1 ' , , , , ,>I '> , 31. '> , >I

0.001 0.002 0

100

....-.

:::J

0

:I:

"-

en

+-

Q.

E

CI)

-t:::::a

+-

+-

0

<t

""""

CI)

+-

0

a::

CJ'

c

0

U

Average Holding Time (Hours)

Figure 14. Traffic intensity per line as a function of call rate and holding time.
The shaded areas in Figure 15 indicate the approximate operating ranges

for line and trunk traffic for a typical circuit switched network. There

are, of course, overlaps between these two kinds of traffic.

Interactive traffic and bulk traffic operating ranges are also indicate~

on this figure. Again there may be considerable overlap. The interactive

traffic occurs between data terminals that send and receive many messages

with very short durations. Bulk traffic includes file transfers. Here

connections are held for long periods of time, perhaps on the order of hours.

In both of these cases (interactive and bulk), the use of a circuit switched

network' is uneconomical if they occur on a permanent daily basis. -It is

often more practical to either lease dedicated circuits from a carrier or to

use different switching techniques.

4.2. Interface Mul ti plexing andConcentratl ng

One of the potential interface functions. is multiplexing or concentration. It was noted previously that the max tmum traffic intensity offered

per subscriber1s line cannot exceed one Erlang. Several lines can be multiplexed together onto a common transmission or trunking facflity from a remote

cluster of terminals, or at the switch for switching purposes. Such a common

facility cannot carry a load in excess of 1 Erlang/trunk,Blthough its offered

load need not be·limited.

The concentration entails blocking. However, the traffic intensity is

usually much less than one Erlang per terminal. Often it is less than

0.2 Erlangs. Since this t raffic is generated randomly, and full availability

is desired, it is practical to use one or more concentration stages ahead of

the switching matrix. This permits a variety of arrangements of additional

lines to be switched at given times. The network is designed to provide an

acceptable blocking probability to the user. The-concentration ratio used is

on the order of 2:1 to 6:1, depending on the number of lines in the group,

the traffic intensity per line, and the grade of service desired. Also, all

of the terminations to the switch may not basubscriber lines. Usually some

calls are connected to other switches via trunks. The ratio of intraswi.tch

ca11 s to i nterswi tch ca11 s depends on the commmrty of interest served by the

switch. Concentrators may be remoted to areas of high terminal density. The

remote concentration units (RCU) must be designed with an acceptable blocking

41
0.005 0.01 0.02 0.05 0.1 0.2 0.5 2 5 10

0.2

0.1 ' , I , I , 'WI I , ! , , ! I I I , , ! , , , '"N , '-' ! ! ! ! , ! ! ! ! ! ! , I , ,,,,, , , ! ! ! ! ! ! ! !I' ! ! f ! ! a, ! ! ! ! ! ! " ! , , , , ! , ! , '.

0.001 0.002

3.6s 1.2s l8s 36s 12s 3m 6m 12m 0.5h th 2h 5h 10 h

100

50 ~;; INTMACTIVE'''\..~ //~

o~./('

2017-"\.. <, J/J~/~ /~ I~

~~.

,,-- /1-

f. ::::s

0 10 ~~ J: o~ ........

en ~".1 .. J<) 0- 5 ~,-.. E

..

Q) </~ ..

«

-.....

-I=:=:a Q)

N .. 2 0

a::

c

0

u

0.5

Average Holding Time (Hours)

Figure 15. Approximate operating ranges for line and trunk traffic.
probability. Their performance still is a function of the community of

interest in which they serve (see Sec. 5).

When traffic from a number of terminations is multiplexed together, the

traffic intensity in Erl~ngs on the multiplexed output equals the sum from

all input terminations. This is because the ordinary multiplexer allocates a

fixed channel to each and every termination. This allocation ,may be by wire

pairs in a cable (space division multiplexing), by frequencies in a channel

(frequency division multiplexing), or by time slots on a highway (time division

multiplexing). If the average traffic intensity per line is A, then the

multiplexed intensity is MA, where Mis the number~of input terminations.

When traffic from a number of terminations is concentrated, the maximum

traffic intensity at the concentrator output is less than or equal to the

number of input channels. Input channels are allocated dynamically by the

concentrator. Fewer output channels are required, since they are assigned as

needed. When all output channels are occupi~d, new arrivals are blocked.

For a fixed probability of blocking, the output capacity in Erlangs

decreases as the concentration (ratio'of input to output channels) increases.

The effect due to ~ifferent number of sources is indicated in Figure 16. The

curve in the figure shows the traffic intensity or capacity of 10 output

trunks in Erlangs, as a function of the number of input terminations. It is

assumed that on the average 1 in 100 distant calls is blocked and cleared4.

It is seen, for example, that 50 lines may offer 4.5 Erlangs of traffic to

the 10 channels with a PO=O.Ol blocking probability. The average traffic

intensity per input line must theref~re not exceed 4.5/50=0.09 Erlang for the

specified grade of service.

In a digital switching system, the line/trunk interface may include a

coder and decoder (codec) for analog ihputs, and a time-division multiplexer

or concentrator, as shown previously in Figure 12. The output bus from the

concentrator or multiplexer may contain any number of time slots.

First level multiplexers, often used in North America, digitize speech

with a pulse code modulation (PCM) developed for T-carrier transmission

facilities. The codec samples the speech signal 8000 times each second and

encodes each sample with an B-bit binary number. The resulting bit rate for

40istant calls and distant call blocking probability, PO' are defined in

Section 5.2 and in Appendix A.

43
1000 ,---------r---------r--.,..----r-----.....--------

500

100

f/)

G)

o

'-

::J

0 50

en

't0

"-

CD

.a 20 E

::J

Z

10

5

Po =0.01 (Based on Traffic)

2

2 4 6 8 10

1......------'----__...I--------&.-----L-------'

o

Traffic Carried by 10 Trunks (Ertonqs)

Figure 16. The effect'ofthe number of sources on capacity of

10 trunks with 0.01 blocking probability and

assuming blocked calls are cleared.

44
a speech channel is therefore 64 ,kb/s. Twenty-four channels are assemble~

into a frame of 192 bits. One bit is added for frame synchronization, resultin~ ina transmission rateof8000x193=1.544 Mb/s. Control signaling information is transmitted by bor~owing the least si9nificant bit from each channel

every sixth frame. The digital signal- output from this 24":'C'ha-rinel multiplexer

is known as a 05-1 signal. It can be transmitted over a T-l carrier. A

second level multiplexer combines 96 digital voice signals into a 6.312 Mb/s,

05-2, signal, which,is suited for T-2 carrier facilities.

In Europe, a somewhat different scheme has been standardized (see CCITT,

1977a). Thirty voice channels are digitized (PCM) and multiplexed using time

division techniques. Two more channels are used for signaling and synchronizing, bringing the total to thirty-two 64 kb/s channels. The resulting

transmission rate is 2.048 Mb/s~:-

Similar techniques can be used for concentration as for multip1exing~

The concentrator output may use either T-l, T-2, or other transmission

facilities. Digital repeaters may be required when concentrators_are remoted

from the switch.

The curves drawn in Figure 17 show the offered traffic intensity per

line as a function of concentr~tion rates for 4, 10, 24 and 96 channel outputs.

The later two correspond tqT-l and T-2 type carriers. It is assumed that

blocked calls are cleared and the concentrator has a one-way blocktnq probability of 0.01. It is also assumed that each concentration stage has a low

community of tnterest; i.e., inputs are seldom, if ever, connected to other

inputs on the same concentrator.

A concentrator with 96 two-way input lines, and 24 two-way time-division

output channels has a concent~ationratioof four. Referring to Figure 17,

it can be seen for this example that the average traffic intensity per line

cannot exceed 0.2 Erlangs, or more than one out of a hundred call attempts

- will be blocked. For connections involving twoconcentratiofl stages, as is

often the case, the two-stage blocking probability is slightly less than the

sum of the two probabilities. If each has a probability of .01, the twostage blocking probability is roughly .02.

When a concentration. stage serves subscr-ibers with a hjghcommon community

or. interest, the blocking probability is different than that indicated in

Figure 17. This situation is discussed in Section 5.

45
0.01

2

5 10 20 50 >,00°.36
4.3. Traffic Circulation in the Switch Matrix

The digital .swt tch depicted by the block diagram in Figure 12' incorporates

a T-5-T switching matrix. Any combination of lines and trunks can be terminated at the interface and interconnected by the matrix. The matrix is

assumed to have full availability to all access channels. The purpose of

this section is to define the traffic handling capabilities or capac~ty of

the matrix.

The total traffic entering and leaving the matrix during any given

period must be equal. Therefore the total traff-ic carried by the switch is

A = rnA T 2

where m is the total number of access ports on the matrix and A the average

traffic intensity per access port. For a 300 line switch and assuming

0.15 Erlangs/line, the maximum traffi~ carried is the offered load

300;0.15 = 22.5 Er1angs.

This assumes that all t raffic is intraswitch traffic and none originates or

terminates on another switch via trunks.

When trunk traffic is included, the c~rried traffic may be differently

estimated. It depends on how the terminationS are counted. For example,

assume that on the average each subscriber originates 5 calls per hour.

Furthermore, assume that 2 of the 5 calls are to other subscribers homed on

the same matrix (intraswitch calls), and 3 are to other subscribers homed on

a different switch (interswitch calls). During the hour, the same average

subscriber may receive 4 calls, 2 of which are intraswitch calls and 2 are

interswitch calls. Let the average holding time be one minute. Then the

average traffic intensity on that subscriber1s line is as follows.

Originating Intraswitch calls 0.033 Erlangs

Originating Interswitch calls 0.050 Erlangs

Received Intraswitch calls 0.033 Erlangs

Received Interswitch calls 0.033 Erlangs

Total Intensity per line 0.150 Erlangs

The traffic circulation in the switch matrix for this average subscriber

is shown in Figure 18.

If only the lines are counted in sizing the switch, then for a 300-line

matrix the total traffic carried is, as before, 22.5 Erlangs. When the trunk

47
+:::-

co

Per. Line

Intensity

('Erlangs)

0.05

0.033

0.033

0.033

SWITCH" MATRIX

-

- - --

- 1 -

-"- -.....

0.05

0.033

Per Trunk

Intensity

(Erlangs)

Figure 18. Averaget·raffic· circulation per line and per trunk fora specific example.
calls are included in the fixed line load, the carried traffic increases.

Thus it is seen, from Figure 18, that the actual traffic carried by the

switch is

300(0.05+0.033+0.033) = 35 Erlangs.

If all of the line's 0.15 Erlangs were through traffic, then the total

traffic carried by the switch would ~e45 Erlangs.

Figure 19a summarizes this example for all intraswitch, all interswitch,

and combined traffic conditions. In'all three cases, the switching matrix

has 300 input lines and is con~idered non~b10cking. Trunks are added as

requi red. -

When the total number of line and trunk terminations is constant, the

non-blocking switch matrix. carr-res a fixed traffic intensity. This is shown

"in Figure 20, where 'the total number of lines plus trunks is held constant at

300. The traffic tntens i typerTine or trunk is 0.15 so the matrix capacity

is 22.5 Erlangs.

In actual practice ;' the number of trunks may be reduced considerably by

accepting some finite blocking probability for interswitch calls. Forexample, in Figure 19, the 1"5 Erlangs outgoing and 10 Erlangs of incoming

trunk traffic could 'be carried by 28 and 21 trunks, respectively, assuming

blocked calls cleared, ful Lave i labiIfty , and a trunk -blocking probability of

O.DOl •

A set of straight l ines-navebeen drawn'in Figure 21 to relate the call

attempts per hour, per termination, to the number of originating terminations,

for different parametric values of calling~ates or number of call attempts

per hour. The same relationship is shown by "bhe curves in Figure 22, except

the calls per termination is used as the parameter. The.re is a reason for

using both parametric representatioh~. It will be clarified shortly. One

additional relationship is needed: th~ total number of call attempts per

hour versus average holding time, and parametric in matrix capacity. This

relationship is shown in Figure 23. Th~ total number of call attempts handled

by the swi tch depends on' the comnoncontro1 element; i , e., on the processor's

capability. This is indicated by the ordinate of Figure 23. Constant processor capacities appear as horizontal lines across this figure.

49
NON - BLOCKING,

SWITCH MATR IX

300

Lines

22.5E-~--....

22.5E -........--..",-

22.5 E No

Trunks

a) All Intraswitch Traffic

300

Lines

22.5E

22.5E

.............. -

45 E

---'

--... ~.--

22.5E

22.5E

300

Tru nks

b) All Intersw itch Traffic

35 E

20E 10 E

300

Lin es

25E -jI__......--...r------.....-I-....- 15 E

167

Trunks

c) Combined Traffic

Figure 19. Traffic circulation in switching matrix as a function of

community of interest. Line ports fixed at 300 and trunk

ports added for interswitch traffic.

50
NON - BLOCKING

SWITCH MATRIX

300

Lines

150

150

22.5 E No

Trunks

a) All Intraswitch Traffic

150

Trunks

- -..... 75

22.5 E

- - 75 - - 75

75

150

Lines

b) All Interswitch Traffic

193

Lines

107 64

22.5E

86 43

107

Trunks

c) Combined Traffic

Figure 20. Traffic circulation in non-blocking matrix with total

number of lines and trunks fixed at 300.

51
Total Terminations

20 K 40 K 100K 200 K

1>J!

Q/

C

Q~

/Q~~

N.0t- ~.o1-

~~

~~

0(,.1'

5K

10 K

2K

400 1K 2K 4 K

~o 200 500 1K

100 200

0.2

10020 40

50

,....

'-

:::J

0

':I: 20 <,

(J)

..

Q.

E

Q) 10 ....

<t

-.........

Q)

5 .. 0"1

C

N a:::

C'

c

- 2 =0

u

'-

Q)

..Q

0

(J)

..Q

::s 0.5

en

Originating Terminations

Figure 21. Relating average subscribers call rate to total call attempts.
20 50 100 200 500 1K 2K 5K 10 K 20 K 50K100·K

50 K

I I o~

,-- 20 K ~( 'lJ(.~0 '-

j q (,

0 ~C:J e,v :I: 10 K .~

"- ,'lJ<S'e,'> -~O (/)

.....

a. ~'~flJ

E

5K Q)

.....

.....

<t

.........

U1 Q)

W .....

0 2K a::

0'

c

0 1K

u

0

...

0 500

Originating Terminations

Figure 22. Relating total call attempts to number of tenninations.
0.005 0.01 0.02 0.05 0.1 0.2 0.5 1 o. 2 5 10

~o~.

° "+ I C0.0

0(\ .

/~

r

e.~0"gd'..1

100 K

,.....

'-

:J

0

::I: 50 K <,

(/)

....

Q.

E

Q)

+-

+- 20 K <t

.........

(/)

Q)

... 10K 0

cr

C'

c

-

- 5K

0

U

0'1 - -I::::t 0

...

{!. 2K

s

...

.- 1 K

.c

0

Co

u 500 '-

0

(/)

(/)

Q)

0

0

200 '-

a..

100

0.001 0.002

Average Holding Time (Hours)

Figure 23. Relating processor capabilities to matrix capacity.
The interrelationships between calls per line, number o~ lines (and

trunks), switch matrix load carrying capacity, and proc~ssor capacity are

developed in the next section.

4.4. Interrelationships Between Capacities of Switch Elements

Figures 14.,21,22 and 23 can be combined into a single figure by matching the 'common, abscissa and ordinate scales. This composite, 'as shown in

Figure 24, is useful in evaluating v~rious switch configurations. Also, " . since different manufacturers specify swi tches Tn different ways, the curves

in Figure 24 ~·can be used to convert different specifications to a common

base. Figure 24 also aids in sizing a switc~ing system and in determining

the relationship between processor capabilities, traffic intensity, matrix Oi ~: ).1 -

capacity, and the number of t~rmi~ations. These applicatio~s of Figure 24

are demonstrated by th~ e~amples given in th~.following paragraphs.

Some of the switch characteristics given in Tables 3 ~hrough 15 were

derived with the aid of Figure 24. As example of this procedure, consider

the SL-l digital switch (Telesis, 1976).

The SL-l switch is a PABX. Modular sizing permits applications in the

range from a few hundred to several thousand switch terminations. The

maximum number of terminations is given as 7600. This size is considered

here.

The SL-l concentrates input terminations onto time division multiplexed

loops. The inierface concentrator digitizes voice channels using standard

PCM at 64 kb/s per channel. Each loop has 32 time slots, 30 for traffic, one

for control signaling, and one for spare. The loop data rate is therefore a

CCITT standard but a USA non-standard, 32x64=2.048 Mb/s. A time slot interchange permits switching between time Slots within the same loop. Multiple

loops and a space division network provides large numbers of time slots and

terminations. Time-multiplexed switching permits interchanging channels

between the loops. Large switches combine 16 loops into groups, 12 for

traffic and 4 for service circuits. Very large switches may consist of up to

5 groups. They need additional memory and multiplexers to perform switching

between groups. The maximum size switch therefore contains 30x12x5=1800

traffic channels at the concentrator's output.

55
Total Terminations

('t~/

C

~q

'?~

/0 19~ I

.~ "K;O~ I ..0<9

~~

0".,-.

100 200 400 1K

0.5

0.5h fh 2h

I

0.05 0.1 0.2

72s 3m 6m 12m

100 I ! I r ! !"'\, I.,. I .,. ! > .,

0.001 0.002 0.005 0.01 0.02

501-

3.6s 7.2s 13s' 36s

100 K: '" I\>:

Q)

....., 2·- ro

0:::

bO

r:::

ro

U 0.5

0.2

0.1

100 K

::s

o .20

:c

<,

20. 10l~ 'k ,. " . ~,

E

Q)

.....,

.....,

5

o 500

Q)

u

o

0: 200

en-

(1)

10 50 K 0:::

eo

r:::

_20K

U·

ro 10Kk o:Ct- .......... r::: 2 5K .- 0.

~E:.=(1)

:.c:::= 2K ro « . 0.-

.1KI

(J"l

m

Average Holding Time (Hours) Originating Terminations

Figure 24. Composite of figures 14, 21, 22 and 23 for switch system capacity evaluation.
Each 30-channel loop is capable of carrying 600 ccs (16.7 Erlangs) of

traffic. This is based on a one-way blocking probability of 0.001, assuming

blocked calls are cleared, and 0.0023, assuming blocked calls delayed.

The total traffic carried by the switching matrix is therefore

12x600x5 5 2 = 18,000 ccs or 500 Erlangs

Based on an average holding time of 2 minutes (0.033 hours) per call,

the total number of call attempts per hour that must be handled by the processor is given by:

A 500 A = T =.033 = 15,000.

The number of originating o·r.r~~~j¥ing artempts. per hour-per channel is,

therefore, 15,000+900=16.7. The average traffic intensity per individual

loop channel is 16.7xO.033=0.55 Erlangs.

The results can be approximated using Figure 24. The solid lines in the

figure denote the SL-l(VL) for 5 groups. The dished lines pn Figur~24 are

for the same switch, but wi th a tota1 of 7600 input terminations • The latter

concentration ratio is 7600+1800=4.22. From Figure 24 it can' be seen that

these 7600 terminations may have 4 call attempts per termination and a traffic

intensity of 0.132 Erlangs (4.75ccs) per line, for an average call of 2

minutes.

The characteristics of the tactical sWltchesgiven in Tables 5 and 6

provide additional examples of how Figure 24 may be used, 'The capacity of

the TTC-39 switch are summarized as follows:

Call attempts per hour

Switch matrix load (Erlangs)

Termi nat ions

3,300

180

600.

These capaci ty va1ues are drawn on FjgHY'.~ >~§.:! .;Cqmp}gttn.g the square on

this figure yields a traffic intensity per termination of 0.6 Erlangs. This

corresponds to 11 call attempts per hour per termination with an average

holding time per call of about 3.3 minutes. The dashed lines on Figure 25

are for the TTC-38 (300 line version)~ a tactical switch whose characteristics

are given in Table 5. This switch as a space-divided switching matrix and

5Thi s is the maximum traffic carried if all loops are full. It may never be

achieved' due to availability limitations in setting up the required connections

through the matrix.

57
Total Terminations

5K

Originating Terminations

0.05 0.1 0.2 0.5

Average Holding Time (Hours)

0.002 0.005 0.01 0.02

...

::s

o .20

J:

<,

10 l ".. 'J ':DL- a. '" ~. -

E

5 +oJ

Q)

2 a::

OD

c::

50

0.2

('0

U 0.5

o1 I l ' L 'I . ">J ,. ,. L > I :

100'K • <, " , < i I... i < , I

...

o 500

Q)

(.)

o

a: 200

en

Q)

50K

OD

.= _ 20K

U~

ro to Kk

oJ:

1- .......... c: tl 5K ."

.- a.

~·E :.: Q)

:.0::: 2K ('0«

0.- o lKI

01

CO

Figure 25. Overlay demonstrating. capacity of large toll switcb.
uses PNPN diodes for the crosspoints. The basic characteristics are essentially the same as the TTC-39. - The TTC-38 processor is rated at 2700 SHCA

for a 600 line switch instead of 3,300 SHeA given for the TTC-39. This would

result in fewer call attempts per line for a 600 line switch and a somewhat

greater holding time. The traffic intensity for both switches is 0.6 E/line.

This appears high for an average subscriber1s line. However, both switches

are designed for use either as an end office switch or a tandem trunk switch.

Supposedly they could also be used as a combined end office and tandem switch.

Figure 24 can be further exploited to define and to quantify what one

means ~y suc~ terms as a small, medium, large, and so forth, switch -- in

terms of matrix traffic and processor capacity. Several such arbttr-ari ly

sele~ted switch size ranges are illustrated graphically in Figure 26 and

summarize~ in Table 8. It is assumed therein that the average holding time

per call is 3 minutes.

The general framework for processor capability and matrix capacity

limitations, .as introduced in Figure 23, may be easily applied to several

commerCial switches. This is done in Figure 27. The total number of lines

and trunks for each switch are also indicated on this figure. The point

where the processor· capacity and matrix capacity cross is engineered to

reflect reasonable balance. That is, the processor capacity need not exceed

the switch matrix capabilities by more than a safe margin, and vice versa.

The factors which limit the processor1s capacity_are discussed in the

next section.

4.5. Capacity Limitations of the Control Element

The functions performed by the control processor were listed earlier in

Table 2. These functions must be cont~asted with the factors that limit the

processor1s capabilities (see Table.7). In this section these functions and

capability limiting factors are discussed in detail.

The processing element of a stored program control must function in real

time. The processor1s capacity is defined as the highest number of calls

processed in a given period of time. This capacity depends on a number of

factors, such as the nature of the traffic, the architecture employed, the

organization of the stored program, speed of l oqic , and amount and types of

59
Total Terminations

0.002 0.005 O.Ot 0.02 0.05 0.1 0.2 0.5

0.2

0.1

100 K

(J)

Q)

+oJ

ro 50 K 0::

CO

c:

«S U 0.5

'-

::J

o .20

::I:

<,

2a. 10 L "'" 3J.... '\0:. y

E • ,

(1)

+oJ

+oJ

-s

Q)

+oJ

«S

0::

CO

c:

50

'-

o

(J)

(J)

Q)

u

o

'-

a..

_ 20K I ) ) U~ 1 },

_ ::J

«S 0

(5::I:

1- ...........

c: 2 5K .- 0.

~E:.=Q)

:.c 2K «S«

0.-

«S

U

0'\

o

Average Holding Time (Hours) Originating Terminations

Figure 26. Switch sizing ,relationships.
Table 8. Switch Sizing Relationships

Total Processor Matrx

Size Terminations Capabilities Capac ty (lines and trunks) (SHCA) (Erlangs)

Very Sma 11

120 600 30

Small

400 -. 2,000 100

Medium

1~200 6~OOO 300

Large

4,000 20,000 1,000

Very Large

61
8m 12m . 30m 1h

Large PABX

(3000 Lines + Trunks)

Small PABX

- (150 Lines + Trunks)----

15 K

18 K

40 K

Large Tandem

(60,000 Trunks)

116 K

3300

1500

TTC-38 (600 Lines)

3700

500 K

360 K

---- ._----------------------- -------

Large Toll

(23,000 Trunks)

I

Very Large PABX

(8500 Lines + Trunks)

Very Large PABX

(7600 Lines + Trunks) ~------ ---~---+---~--_.__._----

Medium PABX

(1250 Lines +Trunks).

TTCJ39 (600 Lines)

3.6s

1M

0.01 0.1

Average Holdinq Time in Hours

Figure 27. Capacity estimates of some commercial switching systems.

62
memory. The .processor capaci ty maya 1so be 1imi ted by overhead' time requi rements. An example of overhead is the line scanning function. Scanning must

be performed continous1y. When the number of lines is increased, more scanning overhead is required and less real time remains for call processing.

Also, the capacity may be reduced as more service features are offered to the

terminals. Thus, abbreviated dialing requires table lookup time. ~f performed often by the processor, it results in fewer total calls in a given

period.

The major factors that limit processor capacity are diScussed in the

following subsections.

4.5.1. Nature of Traffic

The processor capacity'for a given size'switch can be estimated using

the curves in Figure 24. One convenient method is to determine the number of

busy hour call attempts per unit of carried traffic. This, of course, depends

on the average holding time per call. Figure 28 is a linear plot of Erlangs

per call attempt versus minutes per call. The slope of the line is 0.0167

Erlangs per call attempt per minute. Experience has shown that for each

.05 Erlangs of traffic carried by the matrix, there corresponds a processor

work load equivalent to one busy hour call attempt. This amounts to an

average holding time of 3 minutes (Fig. 28).

Table 9 'lists the total number of switch terminations which can be

handled by a control processor limited to 10,000 busy hour call attempts.

The values indicated can easily be estimated from Figure .24. Table 9 shows,

for example, that 10,000 terminations, each carrying 3-minute calls that add

up to 0.1 Erlangs, can be handled by t~e assumed processor. The switch

matrix for 10,000 terminations carries 10,000xO.1 72=500 E (see Sec. 4.3). If

the rule of thumb of .05 E per call attempt (see Fig. 28) applies, the

processor is required to handle 500/.05=10,000 call attempts, as specified.

Under these conditions, the number of call attempts handled by the

processor is comparable to the total number of terminations. Tables 3 and 4

show. that this relationship is conservative. This is partly the result of

increasing processor capabilities to allow inst~ntaneous peak loads, and

partly due to higher loading on trunking facilities.

Some switching systems are engineered with a 30% processor time' reserve

for peak overload demands (Nowak, 1976). Another 20% may be reserved for

63
o.12·.--........._-~-------r---..-----oop----.----.,.---r-"------T-------.

3 4 5 6

Slope =0.0167

0.08

0.00 ~-----------'-------'------------_--""-_-_'"

o

0.10

0.06

o

U

0.02

U)

g' 0.04

..2

\0-

W

=

...

j

o

:I:

a

E

Q)

....

<i

Average Holdi'ng Time in Minutes

Figure 28. Estimating processor capability requirements.

64
m

01

Table 9. Possible Number of Switch Terminations When Control Processor is

Limited to 10,000 Busy Hour Call Attempts

""-

Average

Holding ..

Carried Time'''':';

Load per Termi- 1 Minute . 2'~:Mi nutes 3 Minutes 5 Minutes 10 Minutes nation (Er'l anqs)

0.05 6,666 13,333 20,000 33,333 66,666

u ,"

0.10 3,333 6,666 10,000 16,666 33,333 .

0.20 1,666 3,333 5,000 8,333 16,666

0.50 666 1,333 2,000 3,333 6,666
fixed overhead functions, not related to traffic load. This leaves one-half

of the busy hour for call processing. The time available to process each

call attempt for a 10,000 termination switch is therefore roughly 180 ms.

A switch of this size may have on the order rrf 10,000 instructions in

the program, of which 60% are devoted to call processing (see Sec. 4.5.3).

The average time alloted per instruction is therefore about 30 ~s in this

exchange.

A large percentage of call processing instructions involve table lookups

and updates. Atypical table search instruction requires 10 read or write

cycles. With the exception of microcycles that consume less than 1 ~sec,

typical cycles tend to consume 1 to 2 ~sec. Thus, the 30 ~sec per inst~uction

appears reasonable. Larger programs may be required for special service

features. In that case, either the processing speed must be increased or

the number of terminations reduced (see Sec. 4.5.5).

4.5.2. Control Architectures

In any circuit switch, the control element performs specific functions

based on received signaling information. 'Call processing functions include

recognizing a request for service, registering the directory number, translating these numbers into routing information, and creating a common path

between terminals ~y activating the switching matrix. In addition, the

processing element performs maintena~ce and administrative functions.

In stored program control systems all of these functions are performed

by software logic programs and computer processing equipment. These control

processors may be implemented using various architectures, as illustrated in

Figure 29.

The control processing architectures can be divided into two broad

categories, centralized and distributed. In the centralized approach, a

single processor performs a multitude of tasks. In the distributed approach,

multiple processors perform one or more individually assigned tasks either on

a fixed or dynamic allocation basis.

Centralized architectures usually provide a duplicate processor for

reliability. This redundant processor may share the work load or be operated

on a standby basis.

In the distributed architecture, the processing functions are partitioned

into tasks that can be handled individually by separate processors. These

66
NETWORK

CONTROL

1

TEMPORARY CPU PERMANENT CAll STOR E

a) Centralized Control Element

NEllOR K

CONTROL

--

TASK A TASK B TASK C

fLP J-LP JLP

MEMORY MEMORY MEMORY

b) Distributed Control with

Fixed Task Allocation

NETWORK

CONTROL

J-LP

EXECUTIVE

JLP

p,P

COMMON

MEMORY

J-l. P

c) Distributed Control with

Dynamic Task Allocation

Figure 29. Possible control element architectures for stored program

controlled switches.

67
processors may share a common memory- or have their own associated memories,

such as in the multicomputer approach. Multicomputer systems often have one

microprocessor which assigns tasks to the others.

Distributed systems, th~t oper~tewith a fixed allocation of tasks,

often incorporate separate processors for reliability: either one for one,

or one for many. Dynamic assignment architectures require less redundancy to

achieve the reliability.

The- centralized architecture is commonly used in both older and larger

switching systems. As the size is reduced, the larger more centralized

controls tend to increase the cost per line. Distributed architectures may

then be more cost effective. Just where the break point occurs is not

clear. Distributed architectures have been used in systems with a few thousand terminations. Other benefits attributed to distributed architectures

include increased call handling capability and a reduction in the amount of

information transfer between switch elements. A possible disadvantage is the

typical need for more software development.

4.5.3. Software Organization

In an SPC switch, the software programs can be divided into four basic

categories, as shown in Table 10. The number of instructions in each category

depends on the type of switch and the features and functions offered. Almost

half of the total program may be used for diagnosing faults in peripheral

equipment, trunk or service circuits, the processor itself, and for miscellaneous test purposes. Some of these diagnostic programs may be stored in an

off-l~ne device, such as magnetic tape, and loaded when needed.

The operating system programs provide task scheduling and control of the

input/output interfaces. The application programs provide call handling,

while the administrative programs provide system support in terms of program

modifications,_data updates and accounting functions.

The total number of instructions/program for some- commercial switches

are plotted in Figure 30. The data points represent different kinds of

switches with different word sizes. In general, the number of instructions!

program increases with increasing number of terminations. This is expected

for the diagnostic portion. The application program size varies with the

number of features and functions offered. Usually, larger systems offer more

service features and administrative functions.

68
Table 10. Software Categories

Operating System Program

o Task scheduling

o Peripheral control

o Work coordination

Application Program

o Call processing

o Traffic flow control

Administrative Program

o Software modifications

o Data base updating

o Accounting

o System monitoring

Diagnostic Programs

o Fault detection

o Maintenance

o Miscellaneous tests

69
lOOK

I I I I I I

I I

~rge Medium

50K l- I EnOffice I

End Office

Tandem/EO

I 0 20K I-'

Medium

10K I

End Office (J)

c

0

e.;:

0

C

ee 5K

'-

2K~ .....

0 0 \- Small ""'-J Q)

0 ..Q End Office E

::J

Z 1K

500

200

5K 50 K 100 K 200 K 500 K 1M 2M 5M I ' I

2K 10 K 20 K

Instructions per Program

Figure 30. Program size for some commercial switches.
In the past, ,the programs for most switching systems have been written

in assembly language. The software development effort for a typical switch

family may be broken down roughly as follows:

Analysis and Design 30%

Coding 25%

Debugging 45%

The program development for one SPC system (No. 1 ES5) is summarized in

Table 11 (Harr, 1968). The first two lines of this table are on-line programs

prepared in assembly language. The number of debugged words per man-yearis probably somewhat low. A more typical value is on the order of 1000 words

or 1ess per man-year,.. _

Table 11. Software Development fo~ No.1 ESS

Program Words per

Software Programmers WOrds Man-years Man-year

Operation 83 52K 101 515

Maintenance 60 51K 81 630

Compiler 9 38K 17 2230

Translation 13 25K 11 2270

The compiler and translation programs in Table 11 are off-line programs

and may have been partially written with a higher level language. The use of

such compilers results in increased productivity per programmer (perhaps as

high as four times).

The use of higher level· languages fo~ on-line programs appears to be

evolving slowly. The number of debuqqed words per man-year for high-level

languages is probably about the same as for assembly language. However, the

program productivity increases since fewer coded instructions are needed per

program function. When the high level code is compiled to assembly language,

additional overhead occurs. This transition tends to increase the operating

time as much as 30%. It is the main drawback for using higher level languages.

ManY,recent basic concepts and techniques, that have developed for

programming computer-control led switching systems, are described by Hill and

Kano (1976).

71
4.5.4. M~mory Size --

The proc~ssor memory size tends to increase as their capability increases.

This ~s indicated in Figure 31. The memory requirements in words, versus

number of call attempts per hour, are plotted for selected number of commercial switches. The points must be properly interpreted, s~nce the word

size varies between certain switches. In general, the word storage tends to

be ten times the processor capacity (in call attempts/hour).

4.5.5. Service Features

In a stored program controlled switching system, the processor's activities can be divided into three task areas:

1. Continuous, constant rate overhead tasks which are independent of

traffic; e.g., line and trunk scanning.

2. Intermittent call processing tasks which occur randomly, but increase

with traffic; e.g., address translation and path selection.

3. Deferrable tasks, which can be accomplished during off-peak traffic

periods; e.g., routine maintenance and administrative tasks.

The manner in which these tasks are scheduled impacts the demands on

processor capaci ty. The number of ca11 process ing ·tasks and the time requi red

to perform each task ultimately sets a limit on the processor's capability.

This limit may be defined as the maximum number of calls which can be processed

in some f ixed interval of time wh'ile meeting all the performance objectives

(Brand and Warner, 1977). A major consumer of processor capacity is the

service feature set offered to the customer. The number and kinds of service

features available is one of the advantages of SPC switching. Features can

easily be added or changed by program modifications via attendant consoles.

Special station apparatus may be necessary to take full advantage of the more

advanced features. Table 12 lists some of the basic and enhanced services

listed in a-typical manufacturer's sales .brochure.

In the military switching environment, additional software packages!

could be added to provide new services, such as precedence, preemption, and

restricted access to assigned groups of users. Security and prtvacy may

also be required for specific calls.

72
10M iii ii, iii, iii.

5M

2M lf/)

I

'"0 1M '-

0

Very Large

Very Large

c:

PABX

Toll

'"C

X

0

a>

'-

la>

as -. 0

!fl:: 200 K

'-J :~

I

w '-

........

0

E

PABX

Q)

. 500K 1M

X Estimated

2K 5K 10 K 20 K 50 K 100 K .200 K

Mo~ular

PABX"

50 K

I

0

I

20 K

tOK

100 200 500 1K

Call Attem pts per Hour

Figure 31. M~mory requirements versus processor capability.
Table 12.

Basic Features

(Standard Apparatus)

o Ring again

o Call transfer

o Conference

o Call waiting

o Call pick-up

Selected PABX Service Features

Additional Features

(Special Apparatus)

o Call waiting

o Call forward

o Manual intercom

o Abbreviated dial

o Automatic dial

o Extension override

Special feature requirements can affect the processor's capability. The

call processing time increases as features are added, thereby reducing the

number of call attempts handled in a given period. The capacity limit of the (:--).

switch depends on the mix of station apparatus and special features employed.

This is illustrated by Figure 32 where the total processor activity time is

divided into overhead time, which is independent of the traffic load, call

processing time (which depends on traffic load), and maintenance time. The

fixed or recurrent overhead time depends on the type of switch. The overhead

may vary depending on the particular application of the switch. In a given

application, the processor must continuously perform certain functions such

as scanning the lines and trunks, and monitoring status regardless of the

traffic load. As the traffic load increases, call processing activity time

exceeds the basic overhead time. At lower traffic, deferable tasks can be

performed to fill the available time. Ultimately, as more and more calls

arrive, the processing time increases to a point where handling of additional

calls becomes impossible. Usually, such switch congestion violates some

service criteria (e.g., dial tone delay)'. The traffic then has exceeded the

capacity limit. This limit can vary by as much as a factor of two or more,

as the mix between standard and special features changes. Addition of special

features to a given switching system reduces the number of terminations the

switch can handle.

74
100%

Q)

E

i=

...

>

...

0

«

....

0

fI)

fI)

'.J Q)

01 s....

a.

--------- -~- - - - ------

'1111' M~?~;::~I~e 8: 0 //~~{:f_11111 Time ~, :. vP/~////

.i: 'J!!I////~ ~-"/////////I' : 0' TIme ,

Variable Overhead Time

I . .

I

I

Fixed Overhead Time

I

OOA I o I I

Capacity

Limit

(Full Features)

Increasing Traffic Load ..

Capacity

Limit

(Basic Features)

Figure 32. Impact of s~rvice features on processor capacity.
4.6. Control Signaling Systems· Impact on Capacity

Signaling systems provide the means for remotely controling the switching system. In this section, one is concerned with signaling techniques used

on both the line and the trunk sides of the switch. Station signaling on the

line side and interswitch signaling on the trunk side may take various forms.

There may be in-band or out-of-band signaling on analog c~rcuits. These may

be in-slot or out-of-slot signaling on digital circuits. A review of various

control systems which exist today or are contemplated in the near future is

given by Linfield (1979). In this section, the impact of some commonly used

signaling systems on the capacity of a SPC switching system is dis~ussed.

4.6.1. Station Signaling

The call handling capacity of an SPC switch varies with the types of

station apparatus, the call mix and, as noted previously, the service features

offered.

The station apparatus types include rotary dialing or dual tone multiple

frequency (DTMF) dialing.

The DTMF dialer uses 10 out of 12 standard push buttons to send combinations of address digits, 0 through 9, using a code consisting of two in-band

frequencies emitted simultaneously. The additional buttons may be used for

special services, such as priority calling. The time for the dialing operation

Increases by about a factor of two over DTMF when a rotarydi a1 telephone is

used. The rotary dialer emits a controlled sequence of dc pulses on the

subscriber·s line. The number of pulses between breaks corresponds to the

decima1 digit, except that lOpulses are used for the 0 digit.

Table 13 summarizes the time factors involved in accessing the telephone

network. The connect time increases for interswitch calls, because the

processing times for each switch in tandem are additive.

A number of tone generators, registers and senders from a common pool

are usually shared at the switch. On the average, that decreases the total

switching time. Incoming calls are held in memory by the processor until

the appropriate common equipment becomes available. This queueing for

service equipment provides some smoothing of the offered load bursts. It

permits the processor to handle simultaneous calls in sequence, and increases

the effective processor capacity.

76
Table 13. Representative Values of Contributors to Telephone Network

Access Time

Dial tone delay

Light traffic

Heavy traffic

Dialing time

Rotary

DTMF

Connect time

Local calls

Trunk ca11 s

0.1 s to 0.5 s

0.1 s to 100 s

10 s manual

4 s manual, 0.7 s automatic

1s to5 s

lOs to ]:~, s

The average amount of time pereall required by the processor also

depends on the call mix offered by the. stations. Call mix varies as a function of local subscriber population. Nominal call percentages at a com~

mercial switch are asfollow~:

Completed calls 60%

Busy and no answer '20%

Improper dialing 15%

Other (includes blocking) 5%.

The number and types of service features requested also impact the time

per call, as noted in Section 4.5.5.

The station type, call mix and features offered all jointly determine

the number of instruction cycles .tha t must be executed to process a call.

This was shown earlie~ in Figure:32. The average time pereall increases as

features are added, decreases as -OTMF telephones are added.

4.6.2. Interswitch Signaling

Interswitch signaling provides communications between processors in SPC 'I

switches. In the past, this has commonly been accomplished on a per-trunk

basis. More recently, common-channel signaling systems of various forms have

been introduced (e.g., CCIS, CCITT No. 6,CCITT No.7) for use on public

switched telephone networks. Common~channel signaling techniques combine the

signal requirements for several channels onto a single separated signaling

77
channel. Common-channel signaling can also be used between remote concentration points and the switch and on multiplexed buses within the switch itself.

Since common-channel interswitch signaling (CCIS) has several advantages

over per-trunk or per-channel signaling, this technique will be discussed

next. Emphasis here will be on its impact on switch system capacity.

A block diagram of a common-channel interswitch signaling system is

shown in Figure 33. The control information to be transferred between processors is usually delivered "In paral le l " to' the signaling terminal. The

information is formatted into blocks called signaling units (SU·s), with

different SU·s coded for different types of information. Check bits are

added for error control. Figure 34 illustrates several SU·s used by the eCIS

system of North America. Each SU contains 20 information bits and 8 check

bits. The CCIS steps involved in a successful completion of a 10-digit call

are shown in Figure 35.

The traffic intensity of the common signaling channel, As' depends on

the number of trunks being serviced, the average trunk intensity, A, the

average signaling message length, t (in bits), and the signaling rate, c, in

bits/sec.

The signal channel intensity can be expressed as

As = As tIc,

where l/c is the average holding time per signaling message and ~s is the

arrival rate of the message. If each SU is 28 bits in length (see Fig. 34)

and an initial call set up requires 6 SU·s, then the average holding time per

call on a 2400 b/s signaling channel is

t 6x28 C = 2400 = 0.07 s.

Assume that the largest tr~nk group contains 10 channels and each channel

carries 0.7 Erlangs of traffic (0.35 in each direction) with an average

holding time of 3 'minutes. Then the total number of call attempts to be

handled by the signaling system is given by

As = 10 x ~8~ = 0.0388 attempts/so

The signal channel intensity for 10 trunks is therefore

As = Asxt/c = .0388x.07 = .00272 Erlangs.

78
LINES'

TO

TERMINALS

SWITCH

NETWORK

CONTINUITY CHECK

TRANSCEIVERS

TRUNKS

•

•

•

SWITCH

NETWORK

TRUNKS

TO

OTHER

SWITCHES

"J

c.o

SIGNALING

TERMINAL

INTERFACE I .,INTERFACE

EQUIPMENT .. EQUIPMENT

\ I

TRANSFER LINK

\ /

DATA LINK

1_ SIGNALING

TERMINAL

TO

OTHER

SIGNALING

LINKS

\ I

SIGNALING LINK

Figure 33. Control signaling via common channel signaling link.
BIT NUMBERING SC.HEME

HEADING I SIGNAL INFO. BAND NUMBER CKT. NO. CHECK

LONE SIGNAL UNIT (LSU) or INITIAL SIGNAL UNIT (ISU)

'I I. 0I SIGNAL INFORMATION I CHECK I

SUBSEQUENT SIGNAL UNIT (SSU)

o ACKNOWLEDGEMENT INDICATOR ACK. NO. I BlK. NO. CHECK'

co

o ACKNOWLEDGEMENT SIGNAL UNIT (ACU)

II ... I I I0 •..• I I I I 0 I. I· I 0 0 0 I §] SEQ. NO, .. 1 ~HECK I

SYNCHRONIZATION SIGNAL UNIT (SYU)

II I I I0 I I I I CONTROL INFORMATION I CHECK I

SYSTEM CONTROL UNIT (SCU)

I I SIGNAL INFO. BAND NO. or MISC. INFO. MGMT. INFO• CHECK

. ONE UNIT MANAGEMENT SIGNAL

Figure 34. Basic format of signal units used with common channel interoffice

signaling ·system.
ORIGINATING PROCESSOR I DESTINATION PROCESSOR

x

X

FILLER I I COMPLETES DESIGNATED TRUNK LOOP

----------------------~----------"---"------------~

CHECKS' CONTINUITY .__ __ _- __ __ __ __ --+- __ __ __ __ __ __ __ __" __ __ __ __ __ __ ---Jx

LSU I 0" 00 I0 "0 0"1 t TRUNK DESIGNATION I I CONFIRMS CONTINUITY

CONFIRMS ADDRESS COMPLETED --~----------~I---II 0 01: I I I I:':() ..():. 1I TRUNK DESIGNATION I . _.-

0::>

...... AUDIBLE RING RETU.~:NED, -.".~ - ••. - .,-.. " - - T-.";.- -."-: -..- - - - - ,-. - - - - CUSTOMER ANSWERS, STOP RINGING

----~I--IO 101:I () () () I TRUNK DESIGNATOR, CALLED CUSTOMER HAS ANSWERED, : : :1 J

BEGIN CHARGING

CALLED CUSTOMER HANGS UP

STOP CHARGING, RELEASE BACK I [0--'-0)--::': I I I () I -.:()!I TRUN~ DESIGNATOR ---- CONNECTION

LSU 10 ;00(110 0 ·ol TRUNK DESIGNATOR I I RELEASE, FORWARD CONNECTION

READY FOR NEXT CALL

Figure 35.

I I0 I 0 I0 I I 0 I TRUNK DESIGNATOR I LSU

Steps requi~ed for lO-digit call using eels.

"",,"

<,
A single signaling channel may carry 0._.01 Erlangs with a blocking probability of 0.01, according to Erlang B blocked calls cleared grad~ of service

tables. The processor, moreover,- can hold arriving calls in memory until a

signa)ing channel becomes available. Under these favorable conditions, each'

signaling channel can be packed to carry up to 1 Erlang. The 2400 b/s CeIS

channel used in North America is designed to handle 1500 trunks. Under the

conditions stated above, the 2400 b/s eelS channel carries approximately 0.4

Erlangs, if there are 6 SU's per message, and 0.8 Erlangs if there are 12

SU·s per message.

The traffic intensity on the signaling channel for 10, 100 and 1000

truriks is plotted.in Figure 36 for 6 and 12 SU's.

~ignaling~ system capacity. does not limit- the switch system capacity.

This is shown in Figure 37, where the number of call attempts offered to the

processor, via the common signaling channel, are plotted versus the channel

signaling rate and parametric in carried load. Even when the signaling

channel is limited to 0.1 Erlangs, the number of call attempts is over 80,000

for a 64 kb/s signaling rate. This is the standard rate available in one

digital PCM voice channel.

5. TRAFFIC ENGINEERING

5.1. Needs and Background

The objective of this section is to review traffic efficient design and

use of access area networks. The section deals with common configurations of

user lines, trunks, concentrators, switches, and other service subsystems

that perform the communication and switching tasks required.

Emphasis is placed on the networks' abilities to carry projected telecommunication traffic volumes. Clearly, it is cost prohibitive to engineer

systems meant to handle infinite amounts of traffic. Systems are always

costwise and physically limited, and so is their ability to handle extreme

surges of traffic. Network performance under specified traffic scenarios is

nominally described in terms of "grade of service" (AT&T, 1961; Siemens,

1970; Linfield and Nesenbergs, 1978). Unless otherwise specified, grade of

82
1000.K

,

,

,

,

,

-,

,

,

tOOK

A =0.7

1"' = 180s

-/=6 SU's

--- L= 12 SU's

1000

Trunks

-,

,

,

,

,

1K 10 K

..1..0 I <" i i c: i < iii . , , , , , , ,

0.1 I .. ... I 'ta: -4&: I -44: I I I

0.01' /% • "

0.001 . , , , , ,., , '..' a , 'a''''' I ,

100

en

C'

c:

0

-'-

w

c:

--

-

Q)

c:

c:

0

s:

U

C'

c::

c

c::

C'

00

w en

c

0

....

--U)

c

Q)

....

c:

H

<.J

.....

.....

0

'-ISignaling Rate ,e, inBitsper Second

Figure 36. Common channel signaling traffic intensity ver~us signaling rate.
500 1K 2K 5K 10 K 20 K 50 K 100 K 200K 500K 1M 2M 5M 10M

1KI /., £ I L I I I I I , , I ' , I ' ,

100 200

2K

1M

SOOK

I I I ,/ I ,/ ,/ I

~s=i As

200K l- I '\>" / /1 / f = 280 bits

'- ~"\

:::J

.(b

tOOK <..'

0 0'

::r: c;

'-

Q) ~(j Q. SOK ':> U) o· .....

c.

E

Q)

.... 20K

ex> .....

<t:

--

c 10K

.(,)

5K

Signaling, C, in Bits per Seconds

Figure 37. Common channel call attempt capacity.
service refers here to probability of blocking. A typical objective for

commercial and military grade of service may be, a blocking probability on the

order of 1%.

When service requests (i.e.~ calls) encounter blocking, several things

may happen." The blocked calls may be dropped or rerouted (cleared), and thus

lost from the service facility in question. Or the blocked calls m~y be

queued (delayed) until served. In general~ queueing systems include random

delays, possibilities of buffer overflow, and a host of tradeoffs that far

exceed the simpler grade' of service concept and scope (Fry, 1928; Morse,

1958; Saaty, 1961; Kleinrock, 1975; Bear, 1976; and Schwartz, 1977).

Because of space and time limitations, this section will touch delay

systems but briefly. Emphasis will be on probability of blocking effects for

postulated access area subsystems. A summary of the more relevant communications and switching aspects for both the loss and delay system types is

presented in Table 14.

Let us explain the terms used in the table. A serv i ce system or facility

may be first characterized by its general type. It may be called loss,

delay, or some loss-delay hybrid, depending on what happens to typical blocked

service requests. The distribution of service request initiation times or

arrival times plays a major part in determining whether a service process is

at all analytically tractable or not. The Poisson distribution of arrivals.

per unit time is equivalent to exponential, memoryless, or Markov (M) interarrival distribution. It is an ideal model that is' extremely helpful in any

analytical thrust at traffic engineering.

The distribution of service or holding t~~es may also affect the system

performance. Availability refers to the number (or fraction) of serving

trunks which can be accessed by an individual offering trunk (Fry, 1928;

AT&T, 1961; Siemens, 1970). It is simpler to deal with switches, PABX·s,

data buses, distribution modules, and concentration modules that are arranged

to provide full availability.

When faced with delay systems, the order of service, such as first-infirst-out (or FIFO, or strict queueing) versus random order, affects the

delay statistics of specific service attempts. Preemptive (i.e., interruptive)

or non-preemptive priority structures may be required by access area users.

85
Table 14. Methods of System Characterization

System Descriptors

General Type

Arrival Process

Service (Holding) Time

Availability

Order of Service

Random Delays

Buffer Storage

Reroute Provisions

Users or Sources

Servers per Facility

86

Typical or Tractable Models

Loss

Delay

Loss-Delay Hybrid

Poisson (Exponential)

Overflow (Peaked)

Exponential

Deterministic (Constant)

Full

Limited

Order of Arrival (FIFO)

Random

Specified Priority

Probability Distribution

Mean, Variance

Limited (Bounded)

Infinite

Finite

Fixed (Including None)

Adaptive

Infinite Population

Finite Population

Single

Multiple
If delayed, the duration of delay is typically a random variable whose distribution may be hard to ascertain. The mean or the variance may be more tractable, however.

Near the conclusion of Table 14 one finds three numerical descriptors.

The first, the amount of buffer storage, is usually weighed against transmission and switching capabilities. Joint minimization of costs and service

delays is the issue here. The second number mentioned is the user or source

population size. If it is infinite, one may be justified to use either the

ErlangB or the C formula, but only if the system fits the rest of the Erlang

model (Fry, 1928; Morse, 1958; AT&T, 1961). If the number of sources is

finite, grade of service may be found from the Engset results (Riordan,

1962), that aS$ume blocked calls cleared and finite number of sources as part

of the system model. Tables and charts are available for both Erlang Band

C, as well as for the Engset formula (Siemens, 1970; CCITT, 1977b). The

tabulations are classified in ~ccordance with the number of servers, such as

the number of access ports, serving trunks, or the equivalent TOM time slots.

A broad look at the II nowll status of telecommunication traffic engineering

reveals the following. First, the bulk of present R&D activity in this

country and abroad concerns the delay, waiting time, and other queueing

aspects of data oriented networks (Kleinrock, 1976b; Schwartz, 1977). This

is indeed a fast developing field, spurred by packet switching, and rich in

problems and solutions. Second, the older interests in grade of service (9r

probability of blocking) seem to have settled down on a more stable and

comfortably accepted level. This, of course, does not mean that all grade of

service questions are either trivial or readily answered.

Just as in the twenties, when T.C. Fry postulated his eleven General

Assumptions (Fry, 1928), classical blocking concepts are still valid for all

circuit switched, voice and data, systems. Several new and useful tools have

appeared during the last quarter century. The present situation faced by

grade of service estimators is outlined in Figure 38.

The tree chart of Figure 38 shows that exponential arrival and service

(holding) time distributions are by far the most popular and manageable

premises for traffic engineers. Likewise, infinite sources, full network

availability, and systems of the pl.ain loss type (i .e., with blocked calls

87
ARRIVAL AVAILABiliTY REFERENCES

DISTRIBUTION

NONVARIANCE

EXPONENTIAL EXPONENTIAL

COEFFICIENT WILKINSON

INFINITE FULL LOSS

INTERRUPTED KUCZURA POISSON

- FINITE 1--1 FULL LOSS ENGSET KOSTEN

NON

EXPONENTIAL

- INFINITE I-- FULL - lOSS l-- ERLANG B - VAULOT

EXPONENTIAL

(POISSON) ""'" FINITE I-- FULL LOSS ENGSET RIORDAN

EXPONENTIAL .~ LIMITED H LOSS MPJ LOTZE and

FORMULA WAGNER

- INFINITE ,.. LOSS I-- ERLANG B I-- FRY

"- FULL DELAY ERLANG C l-- RIORDAN

CALLS HELD FRY

OTHERS (-POISSON) RIORDAN "- I-- HYBRID NESENBERGS

J- FACTOR PALM

Figur

00

00
lost or cleared) are the easiest to handle. Erlang B, C, Engset, and even

Poisson blocking probability formulas are still quite useful. New variants,

such as the Modified-Palm-Jacobaeus (MPJ) formulas for limited availability,

have been tabulated (Siemens, 1970).

The basic or source references are listed on the right side of Figure

38. Several of' them, such as Kosten (1948-1949), Vaulot (1927), Lotze and

Wagner (1963) or Palm (1937), may not be readily accessible. The work of

Kosten, Vaulot and Palm are summarized in Riordan (1962). The, so called,

MPJ method is described in Siemens (1970}.

Yet, with all these analytical tools, not everything needed is readily

available to both military and commercial telecommunications traffic engineers.

Fo~ instance, ,there appears to be considerable uncertainty about the efficient

planning of server trunks or local tie-lines between a concentrator (or

multiplexer) and its nearest switching node. It is also difficult to depict

adequately the effects of two widely differing user sets (e.g., ,lines and

trunks) on a common m-server ~acility. These two topics will be discussed in

the following two sections. After that~ several other areas of unresolved

traffic issues will be indicated.

5.2. The Server Trunks Between a Concentrator and Its Switch

The efficient use of tie-lines (pr server trunks) between remote or

colocated concentrators or multiplexers (MUX) and their nearest switches,

such as end offices or PABX's, is important to military access area design

because of the number of lines and tie-lines involved. The nature of the

problem and the notation is introduced in Figure 39.

LetM users or sources have access to the high-side of a concentrator

(i.e., to the side with the most ports), On its low-side, let the concentrator

have m server trunks. Typically M>m. The m trunks tie the concentrator to

the switch as shown. By assumption, let there be' no switching at the concentrator. That means that a local, turnaround, call cannot be cross-patched at

the concentrator, but must travel to the switch and back.

The facility shown in Figure 39 is seen to have two types of service

requests. The calls that,~re destined to a distant switch require a single

server trunk. The local calls, on the other hand, require two server trunks.

89
a:::

o

a:::

tZ

LLJ

,<.)

z

8

\.0

a

M

USER

LINES

0-

0-

0-

<,

I "'"

'"

"

~.""",

~/

~""

"

m

SERVER

TRUNKS (--~A-------,

__ _ _ _ _ 1_DISTANT -----CALL__r;

(LOAD A)

SWITCH

or

PABX

- - '_I -----"'"

I. I

Figure 39. The server trunks or tie-lines between a concentrator and a switch

carrying two types of calls: distant and local.
The grade of service, which appears to be di.fferent "for the distant and the ,

local calls, depends on the relative frequencies or mixes of .the two types of

calls.

To proceed, define the following quantities. Let:

a = Distant call load (or intensity) per line

b = Local call load per line

A = Effective total distant load

B = Effective total local load.

Then, as shown in Figure 39, loads aandA~re associated with distant calls

and require one of the m servers. Loadsb and B require a pair of servers.

The key question here is to relate the probabilities of blocking (let Po

stand fo~ the blocking of distant calls and PL for local calls) to the above

loads and to the numbers M and m of users and trunks, respectively.

Without reroute options, the network in Figure 39 is a loss system. If

M is finite, one may consider using Engset tables (Siemens, 1970), but there

is a question of what constitutes the effective load, and what should be the

number of users and servers. The interested reader is dir~cted tfr the

Appendix A where this problem is treated in detail. The dilemma is outlined

in Figure 40.

Figure 40 shows the' total effective load, A+B, versusm, the number of

server trunks, for given Musers and at the projected probability of distant

call blocking of Po=lO-2. The problem is the following. There appears to

exist various blocking possibilities, depending on the relative values of A

and B. Least blocking occurs when all calls are distant (B=O)~ most blocking

when no calls are distant (A=O). And between these two bounds one has a

large region of uncertainty. Without specifying the AlB ratios, a.total load

of A+B=5 Erlangs may require from as few as m=lO, to as many as m=33, server

trunks.

Appendix A attacks this problem inconsiderable detail. While an exact

solution is shown to be difficult, approximations are possible at a cost of a

reasonable computational effort. Typical results are illustrated in Figure

41. This figure assumes that the distant call load is one-third of the local

calls or one-fourth of the total. It also supposes that the probability of

blocking based on traffic observations for distant calls is PO=.Ol. Note:

91
10 20 30

m (number of servers)

0' I I I I I I ,

o

10 t iiiJ '" '" i '" '" i," '" ,"r '" < i

.........- 8 (/)

C)

z

«

-.J

a:::

LLJ

......", 6

CD

+

«

0

« 4 N

s

....J

<X

to

t- 2

Figure 40. Region of uncertainty created by unknown mix of distant (A) and local (8) call loads.
M=NUM.BEROF USERS

12

I I I

PO=O,OI M=40

10 I A I

-:-

B :3 .--...

CJ)

C)

z

<{ 8

--J

a::

I.LJ .....,,'

m

6

0

\.0 <:(

W 0

...J

...J 4 <I

....

0

....

2

5 10 15 20 25 30 35 40 45

m (numberofservers)

Figure 41. Estimated total load vs. number of servers for the assumed practical Po and AlB values.

0' ...-=:: I , I , , I It'

o
The blocking probability, P

L, for local calls is more than .02 for these

assumptions, as described later in Appendix A.

Figure 41 plots ~ndividual curves for the number of users, M=lO, 20, 30,

40, 80, and 00. Each curve shows the load A+B achievable with the number of

servers, m, given in the abscissa. For example, m=24 server trunks can carry

up to A+B=5 Erlangs, total load, if M=40, PO=.Ol, and A/B=1/3. Comparison of

Figures 40 and 41 reveals that the M=40 curve falls slightly below the middle

of the region of uncertainty.

5.3. Common Facility for Two User Types

Flexibility and compatibility objectives of access area subsystems may

call for more than one set of users (sources) to interact with a given server

arrangement. For instance, several CPU access ports may serve the entirety

of programmed PABX actions. There may be more than one memory unit with

parallel provisions for read/write by different user groupings. Both hardware

and software may often be viewed as an m-server facility common to diverse

users.

Figure 42 illustrates three instances of a common m-server facility

serving two apparently dissimilar user sets. In part CAl, a blocking switch

or its main concentration module is fed by L IIlines" that come directly from

user terminals and T "trunks" from a remote line concentration or multiplexing

(MUX) unit. In applications, this wording could be readily reversed. Thus,

the LiS could be trunk and line ports and the Tis could be MUX loops. The

main point is that these two user classes request service from a common bank

of m ports, perhaps outgoing toll trunks. Typically, there may be more

direct station lines (i.e., L>T), but their relative loads are apt to be

lighter. Part (B) of Figure 42 shows a common pool of m signaling units, or

any peripheral equipment, that serves the control needs of L lines on the

local side and T trunks on the toll side. Part (C) of Figure 42 depicts the

recently proposed SENET system model (Vena and Coviello, 1975; Fischer and

Harris, 1976). This model proposes to integrate circuit switching and packet

switching at a common multiplexing or concentration factlity that is intelligent enough to assign m channels to said traffic.

One should observe that the three cases of Figure 42 may involve quite

different service and traffic statistics. For instance, in (A) the service

94
(A)

•

•

•

REMOTE

LINE

CONC.

SWITCH

OR • m

SMART • SERVERS

~~__~CONCENTRATOR •

(8)

L

FACILITY WITH

m CONTROL AND

• SIGNALING UNITS '-

•

• •

•

OJ ITJ···~ •

T

(C)

VOICE

CIRCUITS

DATA

PACKETS

INTEGRATED

CIRCUIT/ PACKET

SWITCHING

CONCENTRATOR

m

CHANNELS

Figure 42. Examples of m-server faciliti~s for two user types:

(a) concentration of lines and trunks; (b) sharing

of signaling units; and (c) circuit and packet

switching integration.

95
(holding) times maybe the same for both classes. In part (C), however, the

duration of data packets may be an infinitesimal fraction of a typical phone

call holding time. In part (B) the service times mayor may not be the same

for the 1ines.. {L) and trunks (T).

Clearly, calls originate at different rates over station lines and

interoffice trunks. Data packets, as in part{C}~ have their own traffic

generation statistics (,Kleinrock, 1976b). There are also issues concerning

blocked service requests. Certain categories of calls can be justifiably

dropped, cleared, rerouted, or pla.lnl yIost. Others-may be queued, such as

perhaps in part (8). And yet others, such;as voice lines in (C) ,may have

preemption priority over data. The general topic extends beyond the scope of

this discussion.

One must stress nevertheless thatth"is,to our knowledge largely unexplored, queueing model could be broadly interpreted and variously applied

to AADSS. The m servers could be tone or ring generators, a bay of operator

consoles, billing and accounting machines, route selectors, not to mention

old-fashioned markers or futuristic s~cure voice encryptors/decryptors,

securedata~Units~stored subroutine lookup and action implementation elements

[such as always needed for various call forwarding, transfers, abbreviated

dialing, conferencing, priority preempting, and other generally or selectively

required AADSSfea'tures and functions (Linfield andNesenbergs,1978)].

This section 'comments briefly on the grade of servi cebehavi or of m

servers that carry'" the traffic of two discernible sets of users. The model

incorporates ar-eal fstic loss-delay hybr-id feature that enables individual

service requests to be either cleared or queued when aJlmservers happen to

be busy. The general nature of the model is seen from, Figure 43. As shown,

the load per line is a. The load per trunk is b. In.typical applications

one envisions a<b and L>T>m, but this need not be a strict universal rule.

For simplicity, assume full availability to allm ..servers from all L lines

and from all T trunks.

The definitions of the loss-delay hybrid has been given elsewhere

(Nesenbergs, 1979). Whenever all m servers are busy - and immediate service

is blocked - the contending user has a choice. He can either join a queue or

he can drop out. To make things simple, both types of users, namely both

96
T

TRUNKS

.\0

........

L

LINES

a =LOAD

LINE

•

•

•

COMMON

rri- SERVER . FACILITY WITH

LOSS-DELAY

FEATURE

r •

l •

•

b = LOAD

TRUNK

Figure 43. Two user types, called lines and trunks, share a common m-server

facility with a loss-delay feature.
lines and trunks, will be assumed to behave in about the same statistical

fashion.' That is, given blocking, all ~equests join a queue land wait until

served) with probability 8. They drop out with probability 1-8 and are lost

(cleared) as far as the common facility is concerned. The random traffic

flow model of the loss-delay hybrid is summarized in Figure 44. In the very

special case when the two user classes merge into one' class (i.e., a=b) and

the number of users is infinite, the probability of blocking is known to be a

hybrid of Erlang Band Cformulas (Nesenbergs, 1979).

The probability of blocking for the common m-server facility, of Figure

43 is treated in detail in Appendix B. Contrary to the concentration/switch

server trunk problem of Section 5.2 and Appendix A, the present problem has

the same blocking probability for both classes of users. A closed form solution for this probability is derived and discussed in Appendix B. We have

computed a few exact cases thereof with a hand calculator. Several bounds

and approximations are also indicated.

The situation is summarized in Figure 45. This figure shows the total

load, La+Tb, that m servers are able to carry at 1% blocking probability. To

get specific numbers, it is assumed in Figure 45 that L=50, T=lO, and that a

and b are such as to equate the line and trunk loads; i.e., La=Tb. Approximate curves are computed for the hybrid loss-delay parameter values 8=0, 1/2

and 1. These curves fall roughly in the middle of a region that is defined

by the so called bounds on m-serverperformance. The bounds are readily

computed, as shown in Appendix B. However, they do exhibit a considerable

region of uncertainty. For instance, when the total load is 12 Erlangs, the

bounds indicate that anywhere from 10 to 20 servers may be required. The

actual value turns out to be astonishingly near m=12. Note, by the way, that

a loss system (with blocked calls cleared) has 8=0 and requires fewer servers

to provide the same grade of service as the 8>0 systems.

5.4. Unresolved Traffic Issues for Switching Networks

The previous two sections have discussed two typical and useful traffic

engineering problems. The resolution of such problems enhances the rationality of design and implementation. They have obvious effects on traffic

efficiency, observed grade of service, the levels of user satisfaction and,

last but not least, the costs of the military networks.

98
Yes

(1-P)

REQUEST SERVICE

FROMAN

AVAILABLE

S,ERVER

RECEIVE SERVICE

(CALL IN

PROGRESS)

No

(P)

Join (Call

Queue Deloyed)

ADVANCE TO

THE HEAD OF

THE QUEUE

WAIT FOR

SOME SERVERS

TO BECOME

AVAILABLE

Figure 44. The traffic flow ~bdel- for the loss-delay hybrid.

ss
8 10 12 14 16 18 20

m (number of servers) ,

2 4 6 00

12

I I I I I I

I "

I

8=0

10 L Jjj 8=1-

2

,-....

(/) 8 =, ~<;) (,!)

z O~ :5 8

c::::

W ~~~ ......." 'va

.0

li:, 6 -a ....J

a

a Q

<:(

0

....J

.....J 4

<:( I / //7 / L = 50

0

~.' I / /// ./' T =10

2- - ~~~ b =50

Figure 45. Bounds and estimated total load (La+Tb) versus required number of servers (m)

for 1% blocking probability, parametric in hybrid parameter 8, and for! the

indicated values of L, T, a and b.
While necessary, the two earlier traffic engineering solutions (i.e.,

Sec. 5.2, &.3 and Appendices A and B) are by no means comprehensive or all

inclusive. They completely ignore the queueing time domain. That includes

all waiting times, random delays, and the storage requirements associated

with anticipated traffic-service processes. The area of queueing systems is,

of course, broad and deep in both theory and appl i cati ons,{Saaty, 1~6l;

Riordan, 1962; Kleinrock, 1975; .Kl ef nrock , 1976b). It is also growing in

impact" on military voice and data telecommunicatioris. For example, to complete

a meaningful buffer sizevs.line provision traqeoff, one has to grasp a

number of tools. They include: network structuring, topological effect~,

capacity assignment options, traffic flow controls, and various alternatives

for time sharing conflict resolution in mul t i access systems. The delay

analysis, which ranges from estimation of average waiting times' to somehow

finding the 90, 95, or 99% occurrence levels for unknown distributions, is

recognized as difficult at best. The analysis often· appears untractable for

rea 1 processes on rea 1 networks. Specia1 chaj.ns of events, such as mi 1i tary

actions, emergencies, peak overload failures, .preempti on , and even priority

queueing, tend only to compound the ~halytical and engineering burdens.

Simulation and observations on existing networks hav~be~n .valuable (Kle inrock ,

1976a;Kleinrock, 1976b).

There are also unresolved issues in the relatively better understood

arena of grade of servic~. One such puzzling, but broadly applicable problem

occurs when a network f act 1i ty must handle at 1east three different kinds of

traffic. The situation tsTl l ustrated in Figure 46.

Briefly, Figure 46 shows a switching network endowed witn two types of

input ports. On the left side there are L lines. On the-~i9~t side there

are T trunks. Service requests specify any of three distinct kinds of calls.

As shown, the calls are denoted as 1I1 0cal,1I IIdistant,1I and IItandem. 1I Local

calls require two lines. Distant calls need one line and one trunk. Tandem

calls use two trunks. The calls encounter a blocking event whenever they

fail to find enough idle lines and/or trunks. For the three kinds of calls,

there are three distinct blocking events with generally different probabilities. Blocked calls are resumed to be clear~d or lost.

When the user population s finite, the problem appears "Eo be a generalization of the rather involved problem discussed earlier in Section 5.2 and

101
T

TRUNKS

o

o

o

o ~--- ----......"

\ LOCAL --- - I - CALL I

" -- --- 1-----.."" ----0 " ", " - ", - /

" -- -- /1' DISTANT

",

/ CAL·L -- -- ""

0---

""

", .,...,.

-"11IIIIo.

- .....

-

.....

- ~---_ ..._-------- TANDEM I

- CALL (

- \

'------------- -

-

L

LINES

SWITCH or PABX

Figure 46. Three kinds of calls through a switching network.

102
Appendix A. To simplify, one assumes here an infinite user population; i.e.,

constant arrival rates for all three call types and under all conceivable

system congestions. One further stipulates that the switch be nonblocking

and with full availability. The call arrivals shall be generated by three

independent Poisson sources, each with its own average rate. The average

service or holding time shall be unity for all call categories.

Initial analysis indicates that this complex problem may nevertheless be

tractable in a formal way. That is, closed form expressions may be feasible

for state probabilities of interest. This includes those equilibrium states

that constitute the three system blocking events. The computational effort

involved in transforming the equations into useful numbers is at present time

unexplored.

Appendix C outlines a preliminary approach to this problem, where, as

shown in Figure 46, three groups of calls compete for the lines and trunks of

a common service network.

6. APPLICATION TO FT. MONMOUTH ACCESS AREA

In the previous se~tions, the parameters which determine a switching

systemls capacity have been identified and some traffic-related performance

parameters derived. In a specific switching environment, such as a military

access area, these parameters can be used to specify the number, type and

size of switching hubs needed to meet the non-tactical communication requirements for that area. One approach to sizing a digital access area switching

system is demonstrated in this sec~ion.

It is important to, define the term lIaccess area. 1I Access areas consist

of military posts, camps and stations t-hat share local communication facilities.

The access area may include t~ctical units and other sub-elements whose

planning and implementation has been the responsibility of a specific military

department (MILDEP)6 or the Tri-service Tactical Program Office (TRI-TAC).

6A recent Department of Defense Directive (Number 4605.5 dated February 7,

1979) provides consolidated unsecure telephone service to DoD components on

a regional bas~s· under a'single management organization, the Defense

Metropolitan Are~ Telephone System (MATS). Tactical elements are excluded.

The area included in a MATS regio~ has a 30-mile radius.

103
Currently, both tactical and non-tactical communications elements (i.e.,

terminals, switches and transmission facilities) in the access area are

analog in nature. However, many of these elements are expected to transition

into the digital world within the next decade. Local access area traffic

that requires regional and intefregional~ccess must interface, at some

.point , with longer haul transmi-ssion facilities. These long-haul facilities

may be commercial carr-ter-s.ur theql obaf -strateqt c Defense Communi cati ens

System (DCS). The wor1dwi de DCSbackbone, network i s controlled and operated

by the -Defense Communications Agency (DCA) for the combined military services.

Figure 47 illustrates a possible hierarchical network structure to

provide access from a milftarybase to the 'global backbone network. In this

example, traffic f'romtermtne lsTs concentrated at a switch hub (PABX) via a

star network. Several switch hubs are connected with a loop network to a

central office on the base. Additional hubs may exist in nearby camps and

stations in a local access area. More central hubs are located at other

military bases in a larger region and one or more of them provides the interregional access viaa long-haul backbone switch.

The hierarchical levels shown in Figure 47 can be related to the, Ft.

Monmouth, NJ, military bases as follows.

Specific Area Examples

European Theater, Pacific

Continental U.S.

Access Level

International

Interregional

Regional

Local

1

2

3

4

Tri-service military bases in NJ

Ft. Monmouth, NJ,Camp Woods,

Camp Evans and CEReOM Building

-5 Post, Camp, or Station Ft. Monmouth, main post only

6 Office Complex Squier Hal l (CSA)

Regional and interregional access facilities for these specific areas are

shown in Figures 48 and 49. Local and lower level access area digital switching and transmission requirements for Ft. Monmouth and its environs are

considered in subsequent subsections.

Figure 48 covers the pmilitary region encompassing Ft. Monmouth and

other military bases in the New Jersey area, including Army, Navy and Air

Force facilities. Switching centers are interconnected by digital T-carrier.

Switch Level

104
Backbone Switch

Regional Switch

Remote

Switch Hub

Communications

Terminal

Regional Access

Area

Figure 47. Hierarchical network configurations for interregional access.

105
To Terrestrial Backbone

(Netcong NJ)

CERCOM

Bldg

Approximate Scale

I I

IOkm

Earle

Naval Ammunition

Depof

Bayonne

Military Port

Facilities

Earle

Pier

Fort

Monmouth

Camp Evans

McGuire

Air Force Base

Fort Dix'

Military Reservation

Lakehurst

Naval Air

Station

To Terrestrial- Backbone Switch

(Cederbrook NJ)

.Fig'ure 48. Regional access to the military reservations in New Jersey area' via T-carrier.

'106
--'

o

'oJ

ApproximateSc·ale·

I I

IOOOkm

Figure 49. Strategic access to digital European backbone via DSCS.
Access to backbone switches is accomplished at both ends to enhance survivability.

Figure 49 depicts a possible strategic aG~ess link from this New Jersey

region to the Digital European Backbone (DEB) via- the Defense Satellite

Communication "System (DSCS), and hence to military bases in Western Europe.

The DEB consists primariiy of 1ine:':'of;:'~.i;ght~icrowave 1inks between backbone

swi tches and repeaters. Troposcatter links permi-t access across less accessible regions to swi tchinq centers in Spain, Turkey, and Africa.

It has been projected that by 1980 ·the~e will be approximately 1500

military access areas worldwide. The number of communication terminal s in

these areas may range f.romsma l l (50 to 300 terminals), to med ium (300-2"000)'

to large (over 2000 terminals) (see Wagner, 1977). Terminal densities in

these areas may vary from less than 10 per square kilometer to lO,OOO'per

square ki l ometer., Tabl e 15 gives estimates of the, number of communicati on

terminals of various types located ona medium size post, a relatively large

access areava.nrili tary region, the cont inenta l United States (CONUS), and

including overseas (OCONUS).

Additional pertinent parameters for planning future non-tactical digital

communications networks are listed in Fable 16.

In the following subsections, the key parameters listed in the table are

quantifi e'C1 for the Ft. Monmouth access area. The area inc 1udes the, rna in

post, adjacent camps and other nearby Army insta llati ons. Swi tchi ng requi rements are determined using the most recent parameter-s. Future growth is not

considered. Several assumptions are made to simplify this plannfng approach.

They are given in the appropriate sections.

One must emphasize that the purpose here is to demonstrate the planning

concept, to indi cate how swi tch hub requi rements can be determined', and to

show how switch capacities may be specified. The results obtained, therefore, should not be construed as a final engineering design. Additional

detailed analysis is required to determine whether subsystems satisfy the

performance objectives and whether final system capacities can meet projected

growth and traffic patterns for the area. Digital terminals and data circuits

are not included in this simplified planning approach. The advent of computer

processing, intel'ligent terminals and automated business equipment is expected

108
Table 15. Es t imates of Military Communications Terminals',

Local to Worldwide

Medium Access Mi 1i.tary CONUS OCONUS

Post Area Region --- ---

Area (km2) 5 50 5,000 15M 500r\1

( ~Jo r 1dwi de)

Population

(Military &civilian) 5,000 15,000 50,000 1.,5M 0.5M

Te1ephone~

Mainline 1,500 6,000 15,000 300,000 50,000

Extensions 1,000 4tOOO 10,000 200,000 30,000

Sub~totals 2,500 10,000 25,000 500,000 80,000

Data Terminals

Interactive 10 30, 100 1,000 400

(' Computer 2 6 30 200 50

,,(, Narrative 5 15 50 500 100

Facsimi.le 3 8 25 250 50

Data 2 6 30 300 50 -' - Sub-totals 22 65 235 2,250 650

Secure Terminals

AUTOSEVOCOM 1 '3 10 1,000 500

109
Table 16. Parameters Required for Access Area Planning

Access Area Profile

o Geographic Area

o Population

o Terminal Types

o Terminal Densities

o Traffic Statistics

Expected Growth Patterns

o Mainline Telephones (basic and enhanced service features)

o Data Terminals and Circuits

Service Features

. 0 Basi·c

o Enhanced

Service Classes

o Normal

0" Restricted

o' Operat~r Assisted

o Maintenance

o Special (digital secure voice terminal)

Performance Objectives Cus.erori ente'd)

o Grade of Service

o Acceptable Delays

o MTTR, MTBF

Trunking Requirements

o Interregional

o International

Commercial

WATS

Specialized Common Carrier

AUTOVON, AUTODIN and AUTOSEVOCOM

110
Table 16 (cont , )

Access Nodes

o Number and Location af Remote Concentration Hubs

o Number and Location of Remote Switching Hubs

o Number and Location of Central Switching Hubs

Switch Parameters

o Subscriber's Lines Served (~penihg)

o Subscriber's Lines Served (ulti~ate capacity)

o Line Distribution for Various Classes of Service'

o Interswitch Circuits, Initial and Final Capacity

o Busy Hour Call Attempts

o Peak Traffic Margins

o Service Features (Basic and'Enhanced)

o Reserve Line, Trunk and Processing Capacity for Traffic Growth

Interswitch Circuits

o Initial and Ultimate Capacity

o Links to Remote Hub and Size of Groups

o Links to Tandem Hubs and Size of Groups

o Special Lines (ernergency, maintenance, information)

o Mode of Operation (incoming, outgoing, both ways)

o Control Signaling Technique

o Type of Transmission Facilities

o Alternate Routi~g

Administration and Maintenance

o Accounting

o Fault Monitoring

o Numbering Plan

o Alternate ,Routing

111
Measures of. Effectiveness

o '. Re1i abi 1i ty

o Availabiljty

o Survivability

o Cost

o Security

o System Life Span

Tabl~ 16 (cant.)

112
to have considerable impact jn the~futureohaccess area-digital ~witching

systems, the network transmission facil'ities, and the users they serve~

6.1. Access' Area Profile

The Ft. Monmouth access area includes the main-post, C~mp Wo6ds, the

CERCOM Building, Tri-Tac offices andother nearby tns te l.l ations .d S shown in

Figure 50. Ft. Monmouth is the headquart.ers of the U.S. Army Communications

and Electronics Readiness Command (CEReQM) and the Communicat~ons Research .

and Development Command (CORADCOM). Other tenants include the C9mmunication

Systems Agency (CSA), the Satellite Corrmunications Agency, elements. of the.

Electronics Research and Development Command,' and the AviationRese~rch and

Development Command (AVRADCOM). The TRI-TAC program office and the JINTACCS

(Joint Integrated Tactical Command and Control Systems) program office are

also nearby.

A map of the main post showing major office complexes, apartment and

barrack facilities, and other pertinent installations is sh~wn in Figure 51 ..

The Ft. Monmouth access area profile information was obtained in an

earlier study by Nesenbergs and Linfield (1976). The demographic: results are

summarized in Table 17; the telephone environment in Table 18; and the data"

circuit inventory and computer facilities in Table 19. Table 20 estimates

the number of terminals by type, to be used in the area around 1985. If this

projected growth should occur (doubling the total number of voice and data

terminals), it would place major demands on the number and capacities of the

switching systems needed.

Using Figure 51 and Table 17, the main post can be divided into SUbareas

'whfch show the population distribution as a function of density. This is

done in Figure 52. Table 21 indicates the density (terminals or drops per

square kilometer) used for each type of area. The table also shows the total

subarea in km2 of each type for the major posts, camps and office buildings.

This density profile is useful for optimizing network configurations and for

arriving at gross cost estimates for the distribution system (Nesenbergs and

Linfield, 1976).

1.13
TRITAC

Office

o

Ft. Monmouth

Main Post

CERCOM

Building

o

1--

Camp

Woods

Figure 50. Ft. r~()nmouth and its envi rons .

Camp

Evans

114
--'

--'

01

Figure" 51. Ft. Monmouth main post.
Complex

Population By Major Office Complex

Location Population

Vail Hall, DCO

Patterson Hospital

Squier Hall, CSA

SATCOM Office

Administration Bldg.

Hexagon

Administration

EW Laboratory

TriTac Office

Main Post

Main Post

Main Post

Main Post

Main Post

Camp Woods

Camp Woods

Camp Woods

New Shrewsbury

116

90

500

350

240

104

2000

260

145

180
Table 18. Ft. Monmouth Access Area Telephone Environment

Station Apparatus By Subarea

Post

ARTADS Camp CERCOM Camp Types TriTac Woods Building Evans Totals

Te1ephones

Matnline 1,775 1,455 1,625 457 5,312

Bridged 2,064 1,059 1,614 401 5,138

Secure 1 1 1 3

Totals 3,840 2,515 3,240 858 10,453

Dial Central Offices

Main Camp CERCOM Camp

Post Woods Building Evans Totals

Designator DCO-l DCO-2 DCO-3 3

(Vail Hall) (Hexagon)

Total Capacity 4,800 2,200 700 7,700

Working Capacity 5,312

Access Area Trunking

Interna1

Special Toll

Commercial Incoming

Commercial Outgoing

WATS Lines

AUTOVON

Total Trunks

351

7

102

70

21

94

645

117
Table 19. Ft. Monmouth Access Area Data Terminal Environment

Data Circuit Inventorl: , ' ,

C;'rcuit Main "Ca'mp·, ·CERCOM Camp

Bit Rate Post Woods Buildi'ng Evans Totals

50 kb/s 2 '" 2

19.2 kb/s 2 2

7.2 kb/s 2 2

4.8 kb/s 7 1 8

2.4 kb/s 3 1 4

2.0 kb/s 1 1

1.2 kb/s 1 1

900 b/s 4 4

134.5 b/s 2 2

100 2' 20 2 10 34

Test 1 10 6 17

Totals 22 31 14 10 77

Large Comp~ter Facilities

Northeast Computer Center

Bldg. 1152, Main Post

Hexagon, Camp Woods

CERCOM Building

Extern~l.Data Services

Computer .Types

1 - IBM 360/50

1 - IBM 360/65

2 - Burroughs 5500

1 - IBM 360/65

Dedicated Lines

Dialup Lines

Total

18

30

48

118
Table Bu. Number and ·Typ~.sof·.Termi·nals··~~~~~~G·t.ed ...,forFt. Monmouth

Access Ar~a ~n 1~e5

Telephones (Mainline)

o Analog (4 kHz) a~ooo

o Digital (64 kb/s) 1,000

o Video (6 Mb/s) 5

Computer Access

o Low Speed (450 b/s) 50

o Medium Speed (3.6 kb/s) 20

o High Speed (48 kb/s) 10

Teletype

o Low Speed (300 b/s) 100

o High Speed (4.8 kb/s) 20

Facsimile

o Low Speed (9.6 kb/s) 10

o High Speed (56 kb/s) "5

o Color (1.5 Mb/s) 5

Television

o CATV (I-way Channels) 8

o Common Channel (2-way Channels) 4

o Slow Scan (2-way Channels) 6

119
--'

N

o

'High

Res'identiol Office

Figure 52. Population distribution for Ft. Monmouth.

k-- 0.5 km -....-I
--.I

N

--.I

Table 21. Terminal Density Profile

Area DensitY2 Subarea Estimate (km2) Tota1 2Area Total

Type Drops/km Post' Woods CERCOM Evans (km ) No. of Drops

Complex 10,000 O. 15 O. 15 0.33 0.05 0.68 6,800

Offi ceo 5,000 0.20 O. 15 ---- 0.05 0.40 2,000

Service 2,000 0.40 ---- ---- 0.02 0.42 820

Barracks 1,000 O. 15 ---- ---- ---- 0. 15 150

High Residential 500 0.50 0.60 ---- ---- 1.10 550

Low Residential 200 0.30 o. 10 -_..- 0.05 0.45 90

High Sub. 100 0.20 O. 10 ---- 0.20 0.50 50

Low Sub. 50 0.10 ...--- ---- O. 10 0.20 10

Totals 2.00 1.10 0.33 0.47 3.90 10,470
6.2. Basic Assumptions and Implementation Concepts

The implementation concept for an all-digital access area network is

illustrated in Figure 53. Digital and analog terminals interface with the

network via concentration units. A time multiplexed loop connects these

units to the switching hub. Repeatered lines may be used for units located

more than 2 kilometers from a digital switching hub. Trunk circuits are also

shown as time division multiplex loops. They can be multiplexed to higher

levels to provide time slots for 24 (Tl), 48 (T1C) and 96 (T2) trunks. Other

details and assumptions made for each subsystem of the network are given in

the following paragraphs.

Remote Switching Hubs (RSH)

Remote switching hubs, like private automatic branch exchanges (PABX),

are located in office complexes and other areas of high terminal density.

All input and outputs from the switching matrix contain 24 time slots. Lines

interface via local or remote concentrators. Intra-area trunks interface

directly (24 channels) or via multiplexers (48 and 96 channels). Some of the

remote switch functions such as fault monitoring, maintenance and diagnostics,

accounting, and other special services are controlled from' a central switch

hub using a common-channel signaling circuit. However, the remote switch can'

serve its subscribers independently, with some reduction in service features

offered.

Switching is performed by the matrix using time slot interchanges on

each loop and time multiplexed gates between the loops, as depicted in Figure

54. The switch size, in terms of number of terminations, depends on the

number of TDM loops used and on the line concentration ratio. The switching

matrix is assumed to be non-blocking with full availability to all lines and

trunks.

Local and Remote Concentration Hubs (LtH,and RCH)

Concentration hubs may be colocated with a switch hub or located remotely

in areas of high terminal density. All typical mainline circuits terminate

on either an RCH or an LCH. The outputs are 24-channel time-division multiplexed loops. Up to 40 lines may terminate on each hub. This provides a

blocking probability of 0.01 for calls to other hubs and 0.02 for local

calls. This assumes that 25% of the originating calls are distant calls and

122
Line Side Trunk Side Line.Side

Remote

Concentration Hubs

Remote

Switching Hubs

T2

T1

Repeatered Trunk

v

Central

Switching Hub

Subscribers

Terminal

l.---..-----.J

Remote

Concentration Hub

Figure 53. Implementation concept for digital concentration,

multiplexing, switching and transmission in the

access area.

123
r Remoted Components .1.. Switching Hub .1

Space

Switch

AVT

TMG,

.....

N

+::-

OT

DVT

T-Trunk

r--. r---,

I...... I I ....;;.I_~_----'

I I I I '--------

~--------,-eI I .' I I -----,-------~t_____.................... L __J L __..J

TRU TIU

Legend

DSVT: Digital Secure Voice Terminal

AVT: Analog Voice Terminal

DT : Digital Terminal

DVT: Digital Voice Terminal

LCU: Local Concentration Unit

RCU:

TRU:

TIU:

TSI:

TMG:

Remote Concentration Unit

Trunk Repeater Unit

Trunk Interface Unit

Time Slot Interchange

Time Multiplexed Gate

Figure 54. Local and remoted components of a switching hub.
75% are local calls; i.e., a/b=1/3. Figure 41, in Section 5, indicates that

under these conditions the 24-channel loop can handle approximately 5 Erlangs.

The average traffic intensity per subscrlber t s line is O.,Ja',~rl~ngs (4.3 ccs).

The traffic intensity in Erlangs which flows through the switching

matrix is derived ustnqFfqureBfi, It tsassumedfbat , dnthe"average 10% of

the calls homing on a concentration unit, are trunk calls,:15%;.are calls to

another concentration unit on the same switch, and 37.5% ~re calling another

37.5% on the same concentrator. This high community of inte:~e-st at the

concentrator level could be expected in an office complex where many interoffice calls are typical. The switching matrix load generate~ by a single

multiplexed loop is the sum of the three types of call; i.e. ~0.5+1.87+0.75=

3.12 Erlangs. It is assumed that all concentration units aresinf Iar, so

that for k such multiplex loops the total switching matrix capacf ty is

k(3.12) Erlangs.

Terminals

The majority of the terminals which interface on a concentret ion hub are

analog telephones. Both 2-wireand 4-wire lines consisting of twisted wire

pairs are used, Station apparatus may provide basic or enhanced service

features depending on the apparatus used and' the interface. Analog-todigital conversion is normally provided by the interface codec., This codec

can beremoted with 4-wire line to the telephone set and commun~cation security

provided with the addition of a COMSEC unit. Data terminals can also be

served using special interface units.. See Figure 54. I~ Section 6.3 it is

assumed that only analog vo tce terminals withbasie service features are

used.

Central Switching Hub (CSH)

The central switching hub provides all of the functions and features of

a remote switching hub. In addition, theCSH is the master control for the

intra-areanetwprk and forinterswitchtrunking. It performs all the local'

administrative functions and provides the access to the public switched

network, specialized' common carrier networks, the Des backbonevand gateways

to other networks. Transmfssion facil iti#es to these external fl~tworks may be

analog or digital. The mode, code and speed conversions are performed by

central switch elements.

125
,Local or Ren,ote Concentration Hubs Sw~hing Hub

37:5CVo

37:5 %

tSC\t/o

0.5 E

O.75E

Trunk

Circuits

Te~"OIS. f DI------------+---------+------o+-----J

o

o '

Figure ,,55.' Traffic flow assumed for remote switching hubs.

126
Control Signaling

It is assumed that the major-tty of the con-trol signaling for 1ine supervision, addressing, alerting, etc. is' accomplished on a per-channel basis.

On digitized voice 'circuits that use PCM, the least significant bit isborrowed from each channel in every sixth frame for signaling purposes. For

data circuits, an 8 kHz signaling channel is, used when digitized voice or

other channels of that rate are available.

Common-channel 'interswitch signal fng is employed between switching hubs .

That common channel is usually equivalent to one 64 kb/s voice ch~nnel. This

provides remote control from the central switching hub tO~~Q_~E!,switching

hub. Signaling to external networks is provided, as requirf!~:,";~7PY' individual • . •·... ···0··:-·, :.~' ..:"',.j',' '-,

networks.

Trunking

Intra- and interarea trunking requirements-have beeri' estimated from the

currenttrunking requirements given in Table 18. Based on this table, the

required percentage of trunk circuits rel atlva-to the total number of main ...

line terminations is as follows.

Remote to CentralSwitchihgHubs 10.0%

Intra-area Switch Hubs 7.0% '

Interregional Switching 6~O%

o Commercial 3~O%

o WATS Line 0.5%

o DCS Backbone 2.0%

o Other 0.5%

It is further assumed that a11 intra- and iriterregional trunks are

multiples of 24-channel digital carriert thus the above percentages can only

be approximated to the nearest upper T-carrier defined in Table 22. The

traffic intensity values for block-ing probabf l'ittes , P=O.Ol andP=O.OOl, are

based on infinite sources, full availabi1itYt and blocked calls cleared;

i.e., on the Erlang B equation. In Section 6'.3, it is assumed that the

intra-area trunks have a blocking probebtl ttyof 0.001.

127
Table 22. Intra- and Interregional Trunking Facilities

Carrier Number of Erlangs Carri~d Signaling

Designator Voice Channels P=O.Ol P=O.OOl Channels

Tl 23 14.5 11.5 1

T1C 47 35.2 30.1 l

T2 95 79.4 70.9 1

Figure" 56 illustrates the trunking requirements derived for the Ft.

Monmouth access-area. Time division multiplexers for high" level carriers are

assumed, but not shown. Repeatered lines are indicated for path lengths

exceeding 2 kilometers. "Access to the DeS backbone is shown as aT2 (96 '.... c· .-;---.

channel) circuit;tbC~derbrook, NJ.An additional T1 or T2 circuit could be

added to Netcong, NJ,for redundancy.

6.3. Digital Switching Requi rements for Main Post and

Nearby In?tallations

The implementation concept described in the previous section can be

applied to the main post at~Ft. Monmouth using the post profile data of

Section 6.1.

A detailed map of the Post was shown in Figure 51. Using an overlay on

a larger version of this map and the information in Tables 17, 18, 19, and

21, one identifies approximate terminal cluster locations for remote concentration hubs and remote switching hubs. This is done in Figure 57. The

central switching hub is located in Vail Hall. It provides the intra-area

and interregional access trunks. The switch also performs local switching

and administrative functions and", when necessary, tandem swttchi ngbetween

other central hubs.

Figure 58 is a composite diagram of the total switching requirements for

the access area with the geographic aspects removed. The switching and

termination requirements are depicted for four hierarchical levels, intraswitch, intra-post, intra-area, and·interregional. Only the mainline telephone terminations are shown on thafi~ure. They total to just over 5300

mainline telephones for the enti reaccess area. The central switching hub

located at Vail Hall provides access t~ telephones in Vail Hall and its

immediate surrounding area. It also provides tandem switching.

128
Cederbrook, N.J.

TRITAC

Office

. Camp

Evans

Eatontown, N.J.

Figure 56. Trunking from main post to environs, Ft. Monmouth, NJ.

129
Camp Evans

.....,

w

o

Autovon Switch

Netcong, N.J.

t Reservation

, _ / Boundary

\'~ . .,,---~,'-'.t-'.", ./ Y \ _,----.--.~ \ . J '/ -_./ d /'1(40) , . - ~--~ \

!4IDA 1,,--,--/' (40)!?:=~CSA~~__ --~TCON (150) ~4O) ,(40)

( ............ SCHOOL (150) \ ..--- - - <)-- ADN. (80) \ 7\

<, \". .". --- \' CERCOM • ,VAIL HALL _-- --- (40) ._-- - (40) \. I \

Building--,---___ ............ 0001.--;:--- -- __.:_------ " -<:J _~.ENG.A.OM. (70) 4km ---.".,. --- . -~+- -~ - --- . /. --:::--- ------~-- ,.,.....,. ,v,...-------, __ -t":-- ~:::::: - - - - / r-------..

_--- '....::.:--, -_ / (40)'·

Camp Woods \-of- \.~.<, .""'J(40) (40) ,,,/ r--·-1. 3km I \.......... \7 <J · t x> y (40) / Legend

TELCOaWATS I <, (~I .-- Eatontown, N.J. I '. ............ I / I-- 0.5 km ..I

+ (/_ / ......\.. \ I .•/ Approximate Scale

'V' <, , \..... \' ../ I 'y ",-'~.' r». "

I 'HOSPITAL12SI'/ 'C:I 1- Central SWitch Unit

I \(350) »: 'v"" 6- Remote Switch Units

[:> 13-Remote Line Unit

( ) Indicates No. of Terminals Served

Figure 57. Concentration, switching, "and trunking on main post, Ft. Monmouth, NJ~
150

75

200

Intrapost

\ TOTAL 'zs,1625

,

\

Wats

Interregional

Autovon

Interarea

, /

/

Intraswitch 40 /

CERCOM I SATCOMJ-J~ 80

1625 LS: ~CSH-2 '\ I I

450 I \\' I ."

rx: H~n \\\. \T2 \\T2 '\, /T1/ /1 Adm. )::s~ 120

840 ~'-'~\: \ / 'I/T1 / 80

Ad.m,' WOOdS, \." '. 'I .,/ RSH-2 150 ~-- ~SH-3 \ \' / /-.'

~'~ / I <, <,T2 \, / -' T1

EW Lab / t ,,\\ I / /

~/ I "" \.1/ / CSA

100 l~ • T1 VaiI'W/CSH1 T1G-. 2-T..!~" . . 80

Hall --- I ---., RSH 3 250 »->: r > \\'" -

-- ..,..T1C /,P \" / ,I \ \ \ <, "T1C

./ / I \ \ \ <,

~,'....> Camp Evans / / I \ \ <, .......Hospital

200 T~/ I I \ \ \ Tl , ~-T1-<:J--2s' 80

/ I, \ RSH-4

, / \ \ 350 75 75.----- \ \ Tl \

TRITAC IJ,

I II \ \ \ School --T1 ~. 40

, ,\ \

/ I \ \ RSH-5 150

/ I I \ \

I \ \Engr: Adm. T1 /"1 'Xl

I I I \ ~=---~ 80

T2J T21 IT,2 \Tl , '\ I I \ RSH-6

/ I \0 / I \

) \

/ \

/

Ii

TOTAL 'IS= 3690

Figure 58. Digital concentration, switching and trunkinq

requirements for mainline telephones in Ft. Monmouth access area.

131
The mainline terminations, trunk circuits, matrix capacity and processor

capacity needs for the six remote switching hubs (RSH) on the main post have

been estimated. The projected requirements are listed in Table 23. This

table also indicates the number of remote concentration units and local

concentration units required for each hub. It assumes that four trunk channels

are required for each concentrator (J.e., 10% of the concentrator1s input

terminations). The table assumes that each 24-channel concentr~tor output

loop carries .5 Erlangs of traffic and that the switching matrix handles 3.12

Erlangs per concentrator loop. Finally, the processor capacity is estimated

to be approximately 20 times the matrix capacity, based on 3 minute holding

times.

These remote switching hub characteristics do not include reserve capacity for traffic growth, nor do they provide processor capacity margins for

traffic peaks. Only the basic features are assumed offered, b~t to all

mainline telephones. The processor capacity would have to be increased as

more full features sets are added.

The factors which constitute the capacity requirements of' the main post

central switching hub are summarized in Table 24. This hub serves subscriber

terminals located in Vail Hall and its immediate area. Its main function,

however, is to serve as a tandem trunking switch for remote switching hubs on

the main post, and for other central offices and hubs in the local access

area; e.g., the CERCOM Building, Camp Woods, Camp Evans and TRI-TAC offices.

At the same time, it provides all switching to inter-regional trunks for the

local access area; e.g., AUTOVON, commercial telephone company, and for widearea telephone service (WATS). Access to the Federal Telephone System (FTS)

is not included. Incoming FTS calls to the area are connected via commercial

circuits.

Table 24 lists the number of terminals served and the number of trunk

channels required from each location. These projected trunking requirements

are approximately the same as those in use now (see Sec. 6.2). Given the

number of trunk channels required, a T-carrier is selected which provides a

sufficient closest multiple of 24 channels. The. capacity per carrier is

obtained from Table 22 for an assumed trunk blocking probability of 0.1%.

The total load carried by' intra-post, inter-area and interregional

trunks is 536.6 Erlangs. Since these trunks handle both originating and

132
w

w

Table 23. Main Post Remote Switch Hub Capacity Requirements

Cone Cone Matrix Processor4 Hub Hub Mainline Loops Trunk Traffi c2 Capacity3 Capacity

Designator Location RCHls LCHls Terminations (T1 ) Channell (Erlangs) (Erlangs) (BHCA)

RSH-l SATCOM 2 - 4 230 6 24 30 18.72 375

RSH-2 Adm. Bldg. 3 2 200 5 20 25 15.60 312

RSH-3 Squier Hall 2 5 280 7 28 35 21.80 436

RSH-4 Hospital 2 9 430 11 44 55 34.30 686

RSH-5 School 1 4 190 5 20 25 15.60 312

RSH-6 Engr. Adm. 2 2 155 4 16 20 12.50 250

0

Notes:

(1 ) 4-trunk Channels per Concentrator Loop

(2) 5 Erlangs per Loop

(3) 3.12xNumber o~ Loops (see Fig. 55)

(4) 20xMatrix Capacity for 3-minute Holding Times
W

Table 24. Ma,in Post Central Switching Hub Line and Trunk Loading .-

Loops or Carried Load Source Terminals Trunk T-Carriers (Er1angs) Designator Location Served Channels Required (/')

OJ Intraswitch c:

e ....

-J RCH Vail Hall Area 40 4 1 3.1

LCH Vail Hall 100 10 3 9.4

Line Total 140 14 if 12.5

Intrapost (-vlO%)

RSH-l SATeOM 230 24 Tl 11 .5

RSH-2 Adm. Bldg. 200 20 Tl 11 .5

RSH-3 Squier Hall 280 28 T1C 30.1

RSH-4 Hospital 430 44 T1C 30.1

RSH-5 School 190 20 Tl 11 .5

RSH-6 Engr. Adm. 155 16 T1 11 .5

Subtotal 1,485 152 8~T1 (equt v. : 106.2

Interarea (-v7%)

(/') CERCOM 1,625 114 T2+T1 70.9 c: Camp Woods 1,540 108 T2+Tl 82.4 :::s

s; Camp Evans 450 32 T1C 30.1

r- TriTac Office 75 5 Tl 11 .5

Subtotal 3,690 259 13-Tl 194.9

(equiv.)

Interregional (-v6%)

AUTOVON Netcong, NJ 2% of 5,315 103 T2 70.9

Commercial Eatontown, NJ 3% of 5,315 T55 2-T2 141.6

WATS Lines Eatontown, NJ 0.5% of 5,315 25 Tl 11 .5

Other 0.5% of 5,315 25 Tl 11 .5

Subtotal 308 14-Tl(equ i v. ) 235.5

Total 5,315 719 34-Tl(equiv.) 536.6
terminating calls, the lo~d carried by the matrix for these trunk calls is

536.6+2=268.3 Erlangs. Adding the 12.5 Erlangs for intraswitch line calls

gives 280.8 Erlangs for the total matrix capacity. If one assumes an average

holding time per call of 3 minutes, then the processor must handle 20x280.8=5616

call attempts per hour on the average.

These results, obtained from Table 24, are summarized in Table 25 for

the CSH. The results from Table 23 for RSH-3 located in Squier Hall are also

summarized in Table 25. Both required and engineered capacities are given in

Table 25. The engineered capacity includes a less-than or equal to 20%

increase in matrix load and processor capability to handle peak traffic

loads. No margin is reserved for traffic growth in this example.

A switch system1s capacity can be estimated as follows. Assume a 3-

minute holding time per call. Then approximately (Sec. 4.5),

Processor Capacity (BHCA) = 10 ATM,

Mat'rix Capacity (Erlangs) = 1/2 ATM.

where AT is the average traffic intensity (or load) per termination and Mis

the total number of terminations. These relationships are plotted in Figure

59. The capacity results from Table 25 for the central (CSH-l) and remote

(RSH~3) 'switching hubs and some commercial and military switch capacity

estimates are also indicated on this figure.

TheCSH-l is primarily a tandem trunk switch. The average intensity per

trunk termination is relatively high compared to the line intensity of terminals homing on RSH-3. The latter, of course, is primarily a line switch

load. The difference is typical for these two switch types. For a switch

with a more equal number of lines and trunks, the capacity requirement can be

estimated by assuming independence and by adding the results obtained for

each type of termination. For example, assume a switch with 200 line termination with 0.2 Erlangs/line, and 100 trunk terminations with 0~5 Erlangs/trunk.

Then, see Figure 59, the following requirements are obtained for'the system.

Required Capacity Lines Trunks Totals

Terminations (Total No.) 200 100 300

Processor (SHCA) 200 500 700

Matrix (Erlangs) 10 25 35

135
Table 25. Summary Characteristics for Central (Main Post) and

Remote (Squier Hall) Switching Hubs

CSH-l, Main Post Required Capacity Engineered Capacity

Line Terminations 140 160

Trunk Terminations '719 816

Matrix Load (Erlangs) 280.8 336

Processor Capability 5,616 6,720

(Call Attempts/Hour)

RSH-3, Squier Hall

Line Terminations 280 280

Trunk Terminations 28 28

Matrix Load (Erlangs) 21 .8 26

Processor Capability 436 523

(Call Attempts/Hour)

136
1K 10K

100 __.....IoA..-~ ..............r......I.-.._-"------a.---L.. --.&....ol~_---...&.__""'----'-...............&o.-.IooooI

100

'-

::s

0

::c lOOK (J)

'-OJ C C- o -0 '- OJ W

-0

C C

0 .- :::I: )(

(J) .~

... ... a. 0

E

OJ

...

...

c::x:

10 K 500 c

c s: U 0

... c en

...

:is .c

o -c a. OJ o

U '-

'-

'- 0

0 u (J)

(/)

Q) -c

c 0 1K 50 0 e ..J a.

Total Number of Lines and Trunks

Figure 59. Relationship between switch capacity requirements

assuming 3-minute average holding time.

137
The switch parameters for this example are also plotted on Figure 59 and

designated EX. The average load per termination (lines and trunks) is found

to be approximately 0.23 Erlangs.

7. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

This report has introduced, categorized, and partly defined the various

switching concepts which are in use today. It has defined the basic elements

of a circuit switch and described the functions the switch performs (Sec. 2).

The perti nent characteristies of severa1 existi ng swi tchi ng systems 'have bl~. j

tabulated (Sec. 3). With this background, the factors limiting the capacities

of a digital circuit switch have been presented. The requirements on switching

~j'stemls capacity are found to be a multi-dimensional quantity involving many

elements of the switch. For a digital switch with stored program control,

these quantities are related to traffic, terminals and control processes. In

particular, in determining grade of service one must emphasize: 1) the

number of terminations served; 2) the traffic load or intensity carried by

the switch; 3) the number of busy hour call attempts (SHCA) handled by the

processor; and 4) the control signaling subsystem (Sec. 4).

The subject of teletraffic engineering has been introduced. This is an

important 'consideration in the planning and conceptual development of all the

network subsystems. The usual grade of service parameter is probability of

blocking. It has been explored for typical situations that arise in digital

switching and concentration nodes. Applicable formulas were reviewed, so

that concentration ratios and switch blocking probabilities can be evaluated

as required. There are, unfortunately, several issues and unsolved problems

in this area. Their access area impact is partly understood (Sec. 5).

Finally, the planning of switch requirements for a specific access area

has been outlined. The approach, applied to Ft. Monmouth, specifies the

required switching capabilities for this post. Certain simplifying assumptions are made. As applied herein, the approach generates the required

capacity information for the design of a· new switching system or for modifications of an existing switching system.

It is concluded that a relatively simple approach may be used for switch

system planning in a given acc~s~ area. The key prerequisite is that the

138
communications profile be known, or that it can be estimated with reasonable

accuracy.

Other key factors which limit the processor1s capacity in a stored

program control switching system are:

Number and Types of Terminations. This includes the data and voice

termination mix, class and service feature mix, and the type of call

mix, such as busy, misdialed and completed.

Processor Cycles per Call. This determines the average amount of time

used per call. The fewer cycles required, the greater the processor

capacity.

Program Organization. The software code and programming language used

for the processor affects the average number of cycles per call and thus

the capacity.

Performance. Network blocking affects processor capacity due to two

reasons. Some time is· wasted in futile attempts. Another fraction of

time is spent searching for alternate routes (if such option is offered).

Storage queues, which sm90th traffic surges, can reduce processor capac~

ity requirements, but only if delays can be tolerated. Even with no

queueing, some capacity margin is needed for peak traffic periods.

Architecture. Processor capacity depends on the method used to allocate

calls-. If more than one processor can share the load during peak

operating periods, the individual processor capacity requirements are

reduced.

Administrative Functions. The time available to process calls depends

on the overhead time required to perform administrative tasks.

Growth. Some processor capacity reserve is often required for future

growth.

Signaling System. The processor may be limited by the control signaling

methodology. On the line side, this limitation is usually due to the

terminal signaling technique; e.g., the address number dialer. On the

trunk side, common-channel signaling techniques appear to be a less

severe limitation.

We have shown how these interactive factors affect the total system

capacity. In some instances, only qualitative results have been obtained.

139
In other important instances, quantitative results have been derived. In the

significant area of traffic engineering, delay systems were not covered due

to time and space limitations. However, blocking criteria pertinent to

digital concentration and switching have been introduced and some important

delay parameter issues described. Since delay effects are important byproducts of queuefng systems, much work remains to be done in this area,

before detailed system specifications can be developed.

When. the concepts and definitions developed in the earlier sections of

the report are applied to a specific access area, many of the results and

objectives are clarified. The Ft. Monmouth access area is used to .demonstrate

how switching needs can be determined for that area. The course indicated in

this report shows how further analysis and planning can be undertaken. Of

course, more refinements are needed before a complete Access Area Digital

Switching System can be specified, procured and implemented.

Some additional studies required for the AADSS development are outlined

below.

1. Establish the non-tactical communications requirements for special

features and switch functions, reliability, availability, security,

and other measures of effectiveness. Apply results to the planning

approach.

2. fxtend switch analysis to provide for growth projections. Include

digital data traffic. Integrate switch specifications and derive

traffic models for various mixes of data and voice traffic.

3. 'Include larger regions (e.g., entire New Jersey area) and multiservice traffic statistics, to extend the analysis beyond the local

access area. Include blocking probability engineering models for a

number of expected communities of interest.

4. Develop traffic analysis specifically tailored for mtlitary access

area. Establish tolerable delays for various classes of service

and evaluate switch capacity objectives in terms of such acceptable

delays. A good example is the access time requirement and how it

is affected by a common signaling channel. Some other unexplored

issues of interest to AADSS are indicated in Section 5.4. The

queueing model described in Section 5.3 also remains to be applied

to the AADSS.

140
5. Include cost as a parameter in development of effective access area

switching hubs.

8. REFERENCES

AT&T (1961), Switching Systems (American Telephone and Telegraph Company,

New York, NY).

Bear,D. (1976), Principles of Telec'ommunication - Traff;,cEngfneering

(P. Peregrinus Ltd., on behalf of lEE, Telecomm.Series 2,Stevenage,

England) .

Brand, J.E., and J.C. Warner (1977), Processor call carrying capacity

. estimates for stored program control switching systems, Proc , IEEE,

65, pp. 1342-1349.

CCITT (1977a), Line transmission, Vol. III, CCITT Sixth Plenary Assembly

(Orange Books), ITU,'Geneva~ Switzerland.

CCITT (1977b), Telephone operation quality of service and tariffs (Orange

Books),. vol. 11.2 and Supplements, ITU,Geneva, Switzerland.

Ftscher., M.J.. ,and T.C. Harris (1976), A model for evaluating the performance of an integrated circuit .- and. packet-switche~multiplex

structure, IEEE Trans. on Comm., COM-24, February, pp, 195-202..

For§;i>e,J.W., and A.G. Nemeth, (.1977) ,An efficient packetized voice/data

network using statistical flow control, Conference Record of International Communication Conf. (ICC 177), Chicago, IL, pp.38~2~44/

38.2-48.

Fry, T.C. (1928), Probability and Its Engineering Use.s CD. VanNostrand

Company, New York, NY).

Gitman, L., H. Frank, B. Occhiogrosso, and W. Hsieh (1977), Issues in

integrated switching network design, Conference Record of International

Conference. on Communications, (ICC 177), Chicago, IL, pp.38.1-36/

38.1-43.

Harr, J.A. (1968), The design and production of real-time software for

electronic switching systems, Proceedings of the NATO Software

Engineering Conference, Garmish, West Germany, pp. 25-30.

141
Hill, M.T., andS. Kano (1976), Programming Electronic Switching Systems,

(Peter Peregrinus Ltd., Southgate House, Stevenage, Hertz. Sgl lHQ,

England).

Joel, A. (1977), What is telecommunications circuit switching, Proc. IEEE,

65, pp. 1237-1253.

Kleinrock, L. (1975), Queueing Systems, Volume I: Theory' (John Wiley and

Sons, New York, NY).

Kleinrock, L. (1976a), ARPANET lessons, Conference Record of International

Commun;cationsConfer'ence(ICC 176}, Philadelphia, PA, pp. 20-1/20-6.

Kleinrock, L. (1976b), Queueing Systems, Volume II: Computer Applicatio~s

(John Wiley and Sons, New York, NY).

Kosten, L. (1948-1949), On the validity of the Erlang and Engset 105sformulae, Het. P.T.T. Bedrift, vol. 2, pp. 42-45.

Kuczura, A. (1973), The interrupted Poisson process as an overflow process,

Bell Syst. Tech. J., vol. 52, pp. 437-448.

Leaky, D. (1977), Switching in space and time, Proc. lEE, 124, pp , 17-24.

Linfield, R.F. (1979), Control signaling in a military switching environment, NTIA Report 79-13, U.S. Dept. of Commerce, National Telecommunications and Information Administration, Institute for Telecommunication Sciences, Available from NTIS, Springfield, VA 22161,

Accession No.

Linfield, R.F., and M. Nesenbergs (1978), Access area signaling and

switching: concepts, issues and alternatives, NTIA Report 78-2,

U.S. Dept. of Commerce, National Telecommunications and Information

Administration, Institute' for Telecommunication Sciences. Available

from NTIS, Springfield, VA, 22161, Accession No. PB 283-464/AS.

Lotze, A., and W. Wagner (1963), Tables of the modified Palm-Jacobaeusloss formulae, Institute of Switching and Data Technics, Technical

University, Stuttgart, Germany.

Morse, P.M. (1958), Queues,Inventories and Maintenance (John Wiley and

Sons, New York, NY).

Nesenbergs, M.(1979), A hybrid of Erlang Band C formulas and its

applications, IEEE Trans. on Comm., COM-27, January, pp. 59-68.

142
Nesenbergs, M., and R.F. Linfield (1976), Parametric cost alternatives

for local digital distribution systems, OT Report 76-95, U.S. Dept.

of Commerce, Office of Telecommunications (now National Telecommunications and Information Administration), Institute for Telecommunication Sciences. Available from NTIS, Springfield, VA 22161,

Accession No. PB258-510/AS.

Nowak, J.S. (1976), No. lA-ESS, A new high capacity switching system,

International Switching Symposium, Kyoto, Japan, pp. 131-1.1/131-1.7.

Palm, C. (1937), Etude d~s delais dat.tente , Ericsson Technics,V.o1.

5, pp. 39-56.

Pitroda , S.G. (1977), Switching systems, Telecommunications, vol. ll, no. 13,

pp. 75-86.

Riordan, J. (1962), Stochastic Service Systems (John Wiley and Sons,

New York, NY).

Roberts, l.G. (1977), Development of packet switching networks worldwide,

International Seminar on Digital Communications, Zurich, Switzerland.

Ross, M.J., A.C. Tabbot, and J.A. Warte (1977), Design approaches and

performance criteria for integrated voice/data switching, Proc.

IEEE, 65, September, pp. 1283-1295.

Saaty, T.l. (1961), Elements of Queueing Theory (McGraw-Hill Book Co.,

New York, NY).

Schwartz, M. (1977), Computer Communications Network Design and Analysis

(Prentice Hall, Inc., Englewood Cliffs, NJ).

Siemens (1970), Telephone traffic theory tables and charts, Siemens, AG,

Munchen, Germany.

Telesis (1976), Special issue on the Sl-l business communication system,

Bell Northern Research Ltd., Ottawa, Canada, vol. 4, no. 3.

Vaulot, E. (1927), Extension des formulas dlErlang en cas ou les dur~es

des conversations suivent une loi quelconque, Rev. Gen. dIElect.,

vol. 22, PP. 1164-1171.

Vena, P.A., and G.J. Coviello (1975), Integration of circuit/packet

switching by SENET (slotted envelope network) concept, Conference

Record of the National Telecommunications Conference (NTC -175),

New Orleans, lA, December, pp. 42-13/42-17.

143
Wagner, L.H. (1977), Access area digital switching system, Proceedings

of Second Annual Seminar, Armed Forces Communications and Electronics

Association, Ft. Monmouth,NJ,pp. 39-57.

Wilkinson, R.I. (1956), Theories for toll traffic engineering in the USA,

Bell Syst. :Tech. J., vol. 35, pp, 421-514.

144
APPENDIXA. DETAILS OF THE CONCENTRATOR/SWITCH SERVER TRUNK PROBLEM

A.l. Problem Definition

Assume the m-serverfacilityof Figure 39. The number of users or

sources is M>m. To expedite matters, consider only exponential 'distributions

for both interarrival times and for service (holding) times. Let bl~cked

calls be lost or cleared without any aftereffect. Let the ,average service

times be unity for both distant and local calls. However, let their average

arrival rates be different. Denote by a the IIdistantll call arrival rate per

user, and by b the 1I1 0calil arrival rate per user. See Figure 39 to emphasize

that distant calls employ a single server and local calls employ two servers.

Finally, assume that the concentrator and the switch have full availability

and that the switch is intrinsically non-blocking (i.e., it has no processor

or real time limitations).

With this convention, one has construed a queueing system of the

M/M/m/O/M type (Kleinrock, 1975), where 0 refers to the total lack of

storage in the postulated loss system. Such systems are known to exhibit

transient and equilibrium behavior (Saaty, 1961; Riordan, 1962; Kleinrock,

1975). Here, one is mainly interested in the steady state or equilibrium

states and their probabilities.

Let the integer pair (i,j) stand for the joint event (or state) that i

distant calls and j local calls are in progress. Then not only Osism and

Os2jsm, but also Osi+2jsm must be true. Let the equilibrium probability of

the state (i,j) be p(i,j). The state probabilities are needed to determine

blocking probabilities for the queueing syste~at hand. The usual way to

find p(i,j)l s is through the flow rate conservation or statistical equilibrium

difference equations for the system (Saaty, 1961; Riordan, 1962; Benes, 1965;

Kleinrock, 1975). The equations are constructed by simply equating the OUT

and IN flows at each(i ,j) state. It helps, however, to first dispose of

unneeded trivial terms. To this end, define

p(i,j) = 0 for all i<O,

for all j<O, (A-l)

and for all i+2j>m.

Also assume for simplicity, that m, the number of server trunks, is an"even

number.

145
For each (i ,j) state not trivially covered by (A-l), the "QUT=IN II

equilibrium equations are:

((M-i-2j)(a+b)+i+jJp(i,j)

= (M-i-2j+l)ap(i-l,j) + (i+l)p(i+l,j)

+ (M-i-2j+2)bp(i,j-l) + (j+l)p(i,j+l),

i f i+2j :s; m-2;

[(M-i-2j)a+i+j]p(i ,j)

= (M-i-2j+l)ap(i-l,j) + (i+l)p(i+l,j)

+ (M-i-2j+2)bp(i,j-l),

if i+2j = m- 1;

(i+j)p(i,j) = (M-i-2j+l)ap(i-l,j)

+ (M-i-2j+2)bp(i,j-l),

if i+2j = m.

There are a total of

m/2. 2 I (2n+l) = (~l) n=O

(A-2)

(A-3)

(A-4 )

linear equations in (A-2),.which is the same as the number of unknown p(i,j).

As is well known, this set of equations is linearly dependent. One of the.

equations may be replaced by the standard normalization,

L p(i,j) = 1.

all i ,j

To solve (A-2) and (A-4) for the (~1)2 unknowns may be a considerable

problem. Consider, for instance, a Tl line spanning given concentratorswitch links. The Tl can accommodate 24 PCM lines. Thus, m=24 may be of

practical interest. But, of course, (2~"'1 )2=169 impl ies a matrix inversion

problem where the dimensionality is 169. For T2=4xTl, the dimensionality of

the matrix is 2401. Furthermore, a single inversion would provide a solution

only for a selected set of values, a, b, M, and m. Thus, an exact solution

to this problem is not at all easy.

146
To proceed, one may attempt to approximate the .ebove exact problem by a

similar, more tractable, problem. In particular, one seeks here an approximating model. that is indistinguishable from the original exact pr~blem for

the three limiting cases: a+O, b+O, and M~. Such an approximating 'approach

is possible, as follows.

A.2. Approximating.Model

Consider the service facility 'shown i·n Figure A-l. One proposes to use

this model as an approximation, to the true physical facility of Figure 39.

Note, first, that for the same (i,j) state the model of FigureA-l has

ei:ther the same number or more idle sources. Its effective load, as well as

its blocking probability, must then be the larger of the two. The new model

therefore provides a conservative design approach to the original model of

Figure 39.

Second, and this shall become clear subsequently, the asymptotic (i.e.,

a+O, b-+O, ~) properties for the state and blocking probabilities are by and

large indistinguishable for the two models.

Third, the new model i's tractable. That is, closed fonn expressions are

possible for all the probabilities of inte~est.

Instead of p(i,j), let the "approxtmattnq" state probabilities be p{i,j).

In accordance with Figure A-l,the P(i,j) are not solutions of (A-2). Rather,

they must satisfy an entirely new set of "approxtmat tnq" equilibrium equations:

[(M-i-j)(a+b}+i+j]p{i,j)

= (M-i-j+l)ap{i-l,j) + (i+l)p{i+l,j)o

+ {M-i - j +1}bP(i , j - 1)+.(j+1)P(i ,j+1) ,

if i+2j s m-2;

[(M-i-j)a+i+j]p(i ,j)

= (M~i~j+l)a~(i-l.j) + (i+l)~(i+1~j)

+ (M-i-j+l)bp(i,j-l),

ifi+2j,=m..1;

147

(A-5)

[con~inued]
SWITCH

OR

PA 8X

LOCAL CALL

(LOAD B)

\

\

\ --~---

\

mServer Trunks

/ --7-

\ --------~

I \

...............

-iM

User I CONCENTRATOR

Lines

--'

..,J::::.

ex>

Figure A-l. An approximate model for m server trunks between a concentrator and a switch.
(i+j)f5(i ,j) = (M-i-j+l )ap(i-l ,j)

+ (M-i-j+l)bp(i,j-l),

if i+2j = m.

There are also (~1)2 equations and (~1)2 unknowns here. The equations

are linearly dependent and require the use of (A-4). The key difference is

that on both sides of the equalities, the factor (M-i-2j) in (A-2) has been

replaced by (M-i-j)in (A-5).

The asymptotic affinity of the two problems is closely related to the

Engsetdistribution (Riordan, 1962; Bear, 1976), especially as it applies

to finite number of sources M. To simplify, assume the following notation

for Engset distribution:

(A-6 )

where n=O,1,2, ... ,m.

Then, when the traffic tends to be all local and a+O, the exact

solution gives

p(i ,j) -+ Ej (~;~,2b)

+ 0

As a+O, the approximate solution tends

p(i,j) -+ Ej(~;M,b)

+ 0

if i = 0,

if i f O.

to

if i = 0,

if i O.

(A-7)

(A-B)

The total offered load in both cases is Mb. For Mreasonably large,

the load is the dominant factor that determines the value of E.(.;.,.).

J Thus, p(i,j) and ~(i,j) are approximately equal for a+O.

When the offered traffic is nearly all distant,b+O. Then the exact

and approximate solutions are indistinguishable in the limit:

p(i , j ), p(i , j) + E. (m ;M, a) i f ~j = 0, 1 ,~

+ 0 if ,jf O. (A-9)

Suppose next that the number of sources is extremely large, but their

offered load is finite. In the limit M-+oo, let lim(Ma)=AO and lim(Mb)=BO'

149
Then as M+B, the two solutions tend to the same, not Engset, distribution

(Bear, 1976):

A i B j o 0

( - I) -(.- -) il j! p .1,J , P 1,J . -+ .. s t'

L AO 80 alls,t sl tl

where i+2jsm comprises the summation domain for (s,t) as well.

Because of the asymptotic properties (A-7) to (A-10), one feels

justified to call ~(i,j) an'approximation of the true p(i,j).

A.3. The Approximate Solution

The formal solution of (A-5) can be deduced by inspection as:

p(i ,j) = -----=--~---

(A-10)

(A-ll)

where the domains of (i,j) and (s,t) are again the same.

To prove that ~(i,j) of (A-ll) is indeed a solution to the approximate

problem~. it suffices to substitute (A-ll) into (A-&). We skip the lengthy

details here. The main point is that ~(i,j), as given in (A-ll), satisfies

all three parts of (A-5).

From the approximating state probabilities p(i,j), one proceeds to

derive the blocking probabilities as functions of the offered load. To do

so, orie must first resolve several relatively minor difficulties with terms

and their interpretation (Cooper, 1972).

First, one can define the probability of blocki~g as either "based on

time" or as IIbased on traffic. 1I If based on time, the blocking event for

distant calls is tantamount to an outside observer finding the system in

the state i+2j=m. Then, PO' th~probability of distant call blocking

must be

Po =1 p{i,j), i+2j=m

and likewise, the local call probability of blocking, PL, must be

150

(A-12)
p = L

m

I p(i,j). i+2j=m-l

(A-13 )

These two probabilities, Po and P

L, are said to be based in time. They

are visible to a completely independent outside observer who monitors the

availability of idle servers at some random times.

A user who is part of the traffic sees a somewhat different statistical

situation. After all, as the number of calls in progress increases, i+2j

grows, there remain fewer idle sources, and the conditional frequency of

call arrivals decreases. Thus, for finite M, more traffic tends to be

generated when the system is less loaded. The probabilities of blocking that

are based on actual traffic percentages, blocked versus carried~ therefore

are slightly lower than those based on percentages of time. The following

heuristic argument gives an indication how the two probabilities may be

related. Imagine that one individual out of the M users is cast in the role

of an "outside" observer. That individual sees, in effect, how the

remaining M-l users congest the facility. Thus, approximately,

PD(Mltraffic) PD(M~lltime),

PL(Mltraffic) PL(M~lJtime), (A-14)

where time-tigged probabilities are the same as given in (A-12) and (A-13).

For practical approximation purposes, the transformation between time and

traffic based blocking probabilities is thu~ straightforward~

The second minor difficulty concerns the effective offered load. For.

well-designed systems, it is only incrementally larger than the actual

carried load and poses no problem. However, the finite source assumption

causes some potential confusion. . .

Let A be the effective total distant load, ,and B the effective total

local load. Then AsMa and BsMb, because the instantaneous arrival rate

can only decrease as more and more calls become active. For the classical

Engset distribution the situation is better understood. Thus, when b=O

(i.e., there is no local traffic and (A-g) i~ valid), one can prove that the

effective distant offered. load is

(A-15 ) Ma

A l+a[l-Em(m;M-l,a)J ·

151
(A-16)

Here, E (m;M-l,a) is nothing more than the blocking loss observed on traffic

m

basis.

Unfortunately, for arbitrary mixes of distant and local traffic, it is

not entirely clear how (A-15) generalizes to relationships between A, B on

one hand and ~1a, Mb on the other. One can, by all means, use the "tn i t ia l "

(i.e., i=j=O) offered loads Ma and Mb whenever expedient. At other times,

when effective offered loads are desired and the blocking probabilities Po

and PL do not exceed 1%, one can approximate the effective loads as

A == Ma / (1+a) ,

B == Mb/(l+b).

The transformation between initial loads, Ma and Mb, and effective loads, A

and B, (A-16), is therefor~straightforward.

A.4. Numerical Results

This section presents numerical calculations done for the approximate

model of Figure A-l. The section evaluates blocking probabilities for the

approximate solution, denoted as p(i,j) in (A-ll). These computations were

done largely on a hand calculator and are rather limited in scope. Neither

the curves nor the numbers should be taken as direct substitutes for the

exact solution. Rather, the approximation should be interpreted as an

indicator of common trends. The eventual goal of these calculations has

been to resolve the uncertainties shown in Figure 40 of the main text and,

if possible, to generate traffic engineering curves of the type presented

in Figure 41.

The initial computed curves, see Figures A-2'and A-3, show approximate

probabilities of blocking tnthe 10-T to 10-3 range. This emphasizes the

broadly accepted practice of seeking grade of service objectives in the

neighborhood of one percent. The-abscissa in both figures is the initial

offered load. Both figures assume a relatively modest number of users,

M=20, and a correspondingly small number of servers, m=lO. Furthermore,

the probabilities depicted (such as Po in Figure A-2) are based on fraction

of time blocked. To translate the results to fractions of traffic blocked,

one uses (A-14). Likewise, either (A-15) or (A-16) should be used to deduce

the effective offered load.

152
M=20

m =10

:3 CD

1 JL = 0 3" b

10-3 'I I I I I

o 2 4 6 8 10 12 14

M (o+b) [Erlongs]

Approximate probability of blocking for distant calls Po (based on fraction of

time) versus the initial load M(a+b) parametric in distant/local load ratio

alb, for M=20, m=lO.

Q)

E

'0

10-2

+=u

c

"- u,

p..0

F.i gure A-2.

..."

0"1

W
M=20

m=IO·

/ = 3 CD

~-I

'0

.2 10-2

....

u

o

'-I.L.

"~ ~t=

.....

t:n

2 4 6 8 10 12 14

M (o s b) [Erlangs]

Approximate probability of. blocking for local calls PL (based on

fraction of time) versus the initial load M(at b} pararnetri'c in

distant/local load ratio alb, for M=20, m=lO.

Figure A-3.
For given values M, m, a, and b, the actual computation for Po is

carried out using equations (A-ll) and (A-12). For PL one uses (A-ll) and

(A-13) .

The results of these initial computations show that both blocking probabilities, Po and P

L, may depart appreciably from classic Erlang and Engset

grade of servi ce curves(AT&T,1961~ Siemens,-1970.).

For nearly all albrO, the blocking of local calls is seen to be

considerably more frequent than that of distant calls. This aspect is

further illustrated in Figure A-4, which directly contrasts Po versus PL

curves. FigureA-4 differs from the previous in several other respects.

The number of users (sources) and the number of server trunks have been

more than doub1ed to ~1=48 and m=24.

Intuitively, one might exp~ct P

L to be roughly twice PO. But things

a're really not that simple. The ratio PL/Po is plotted in Figure A-5. One

sees that PL/Po depends on the ·distant to local load ratio, alb, as well

as on the number of servers m. The points of Figure A-5 are derived from

the same computation that led to previous Figures A-2 to A-4. The two

curves drawn in Figures A-5 are simple graphical fits. As functions of m,

a, and b, they are of the form

~:: 1 85 a 5/m Po + m [m(a+b)] (A-l7)

Note, that for the practical ~ase a/b=1/3 (or a/(a+b)=1/4), the ratio PL/Po

is nearly 2.4 for both m=lO and m=24. The least value of the ratio is unity.

It occurs at a/b=O.

Since the computation of every single p[)'a.nd PL point value is time

consuming, the numerical effort may be r~duced in half through the use of

(A-17) or Figure A-5.

Fora constant offered load, anJncrease in.the .. number of servers,m,

reduces the b16cking probabilities. Buti~for the same constant load an

increase in the number of users, M, doesEhe-oppos i te , It increases the

blocking probabilities. However, the effect of M on Po and P

L is less

dramatic. This phenomenon is illustrated in Figure A-6 for effective offered

load ratio A/B=1/3. The curves, which are parametric in M and m, are not

155
10-1......... iii i, , ,

M = 48

m =24

a

b = (X)

a 1

b="3

Po

/PL ,

Q,)

E

i=

'0

c

o

u

£ 10-2

p.....J

t..-

o

p..0

--'

0"1

<T

Figure A-4.
4r----___,~--___,.___--~.___---..__-- ..

0.8

E =10-2

o

M = 2m

0.2 0.4 0.6

_0_

o+b

The approximate ratio of local a~d distant call blocking prob~bi1ities, PL/PO' for Po~10- and 2:1 concentration

of 11nes.

3

FigureA-5.

, 157
1:0- 1

A 1

T=3

=140

= 70

= 50

M = = ,co CD ••

m-:'24

.Po l 'I. II 1\ N I I) m=36

10-2

2 4 6 8 10 12 14

A + B [Erlangs]

Figure A-6. The approximate distant call blocking probablity PD versus effective total

offered load, A+B, parametric i~ Mand m, and subject to A/B=1/3.
computed on the basis of previous approximations, but instead are the end

result of an even rougher estimate

(A-18)

where E(m;M,A) stands for the tabulated Engset blocking probabt t fty (Siemens,

1970) that is specified in terms of total' effective loadA. The' grade of

service itself (i.e., PO) is interpreted as based on traffic, not time.

Since for M»l the time and traffic bases, are indistinguishable (see (A-14)),

(A-18) may often be used either way_

Several other comments apply to the use of (A-18):

(i) A/B=a/bmay depart from an identity [see (A-15) and (A~16)J.

However, it appears to bea reasonable epprcxtmattcnfnprecttce.

(ii) As A/(A+B) goes fromO tole' ,~he b1o:kin.g pr,~bab.~li~'yPD

traverses its range frOmE(?;~,2BJ~o E(m';~,A)"ina monotonic

fashion. To the extentth~t this transition is not perfe~tly

uniform or linear, (A-18) must be interpreted as an approximation.

Compare Figures A-2, A-3. and'A-4.

(iii)Of the two Engset terms in (A-18), the secotidJet1n.iS usual.ly

the dominant one. If the first te~rnjs'neg1i,gible'" then the'

curves akin to those given i'n'Figure,., 41, of main text can be

simply generated. For ~heas"sumedl'(j(~10-2) and A/B (=1/3)

values, one merely performsan Ehgset table lookup (Siemens,

1970) of Mandrn that satisfy

(A-19 )

A.5. References

AT&T (1961), Switching. Systems (AmeritahTelephbne and Telegraph Co.,

New York, NY).

Bear, D. (1976), Principles. of Telecorilriuh,iCatioh- Traffic'Engineet'ing

(P. Pereqrinus Ltd , , on behalf of lEE, Teleconm. Series 2,

Stevenage, England).

Benes, V.L (1965), Mathematical Theorl ofConnectil1g Networks and te1ephore

Traffic (Academic Press~ New Vork~ NY)~

159
Cooper, R.B.J 19,7Z ),Jntroductionto Queuei ngTheory(MacMill an ce.,

New York, NY).

Kleinrock, L. (1975), Queueing Systems, Volume I: Theory (John Wiley and

Sons, New York, NY).

Riordan,~,J.(J9()2J;, StochasticSeryi~e~Systems (John Wiley and Sons,

N~W york ,:NY) i

SaaFY~ T.L.,09pl), Elements of Queueing Theory. (McGraw-Hill Book Co.,

NewYork , NY).

Siem~ns (1970),TelephoneTraffic Theory Tables and Charts (Siemens AG,

~unch@n, Germany}.

160
APPENDIX B. DETAILS OF THE COMMON FACILITY PROBLEM FOR

TWO TYPES OF USERS

B.l. Problem and Its Solution

Assume the m server facility of Figures 43 and 44. There are two

classes of users indicated. The first class, perhaps too loosely referred '.--. -

to as "lines," contains Lusers. Each of the lines carries an average load'

of a=A1h.l1 Er1angs, where A1 is the average arrival rate and 111 lsthe

average service rate. Under the exponential service time assumption, the

latter implies the average service or holding time to be 1/~1. The second

class, loosely called "trunks," consists of T users, each burdened with

b=A2/~2 Erlangs per trunk. Here, of course, A2 and ~2 have the same arrival

and service rate interpretation as for lines. Note: These loads a and b

shoold not be confused with the other loads, that in the main text or in

Appendix Amay be denoted by the same symbols. Either lines or trunks may be

multiplexed or concentrated on a same bus. In that case, one observes only

the total arrival rates of the two classes, such as perhaps Tb for the data

packet rate [see part (C) of Figure 42, main text]. As in Appendix A, assume

~g~~~ exponential distributions for both interarrival and service {holding)

times. .

Let blocked c'alls undergo the random e versusl-e coin toss implied

in Figure 44. Thus, when 6=1, one has the blocked calls queued or delayed

situation. When 0<6<1 holds, one has a version of the generalized 1055-

delay hybrid (Nesenbergs, 1979).

Let the average holding times be distinct, 111 r112' for the time being,

for the'two user classes. Let their average arrival rates ~lso differ.

Assume again full availability to all servers ~~ ~l.l .users.

Let the pair of integers (i,j) represent the event thatexactly'i from

the lines and j from trunks are either receiving service or are waiting

in queue. Then one must have OsisL and OsjsT.

Let the steady state or equilibrium probability~f event (i,j)

be p(i,j). As in Appendix A,. these state probabilities may be determined

from the flow rate conservati on equati ons. For this problem, the IIQUT=IN"

equilibrium flows at each state (i,j) must be given by:

161
[(L-i)A1 + (T-j)A2 + ill1 + jll2] pC; ,j)

= (L-i+l)A1P(i-1,j) + (i+1)lll P(i+1,j)

+ (T-j+1)A2P(i,j-1) + (j+1)ll2P(i,j+1),

if 0 s i+j < m;

[(L-i)8A1 + (T-j)8A2 + ill1+ jll2]P(i ,j)

= (L-i+1)A1P(i-1,j) + (i+1)lll P(i+1,j) (B-1)

+ (T-j+1)A2P(i ,j-1) + (j+1)ll2P(i,j+1),

lfi+j = m;

[(L~i)8A1 + (T-j)8A2 + ill 1 + j1l2}P(i,j)

= (L...i+l) 8A1 P(i-:l) + (i+1)lll P(i+1,j)

+ (T-j+1)8A2P(i,j-1) + (j+1)ll2P(i,j+1),

if i+j > m.

In this, it is always assumed that p(i,j)~O whenever ~in(i,j)<O.

The number of unknowns,p(i d}, and the number of equations is (L+1)(T+1)

in (B-1). Fortunately, the exact solution can be obtained by simply

postulating that the solution has a separation or product property (Cooper,

1972). We illustrate the nature of this result by working out the details qf

the very fi rst of the three aquat'tonsccntat ned in (B-1). That is, for

Osi+j<m, assume

pC; ,J) = FP1(i)P2(j) , (B-2)

where C is some constant. Then the first part of (B;"l) becomes

lll P2(j){[(L-i)a+i]P1(i) - (L-i+1) aP1(i-1) - (i+l)P1(i+1)}

+ ll2P1(i){[(T..j)b+j]P2(j) - (T-j+l):bPz{j-1) - (j+1) P2(j+1)} = O. (B-3)

Clearly, if the two {... } ,expre"ssiq,nsvanish:, one has a solution. Both

parentheses represent Engset type of state probabilities (K1einrock, 1975).

The complete solution therefore is given by

162
ifO s i+j s m, p(i,j) = (~)(!)aibj p(O,O) 1 J

= (~)(!)ei+j~maibj if m:5: i+j :5: T+L. (B~4) 1 J

The p(O,O) ,factor can be deleted from (,8-4) by the usual normalization

condition that sums all p(i,j) to unity.

Direct substitution of (B-4) into (B-1) verifies that (8-4) is in fact

a valid solution~

The blockfnq probability P for mz l servers follows readily from (8-4). m

Here, Pm will be interpreted as a "fraction 'o~f time" probability. To

interpret it in terms of traffic percentages, the transformation discussed

in ,the earlier Appendix A should be used.

The exact probability of blocking expression (time basis) for the two

user-type problem can be written in several ways:

L+T

p = 2 p(i,j)

m i+j=m

L+T k

= r I p(i,k-i) k=m i=O

L+T L+T

= l. SkI l s., k=m i=O

(8-5)

where the finite sum 5k terms wi 11 be defi ned shortly. They wi 11 turn out to

be convenient to alleviate the computational effort. First, however,

introduce a function that is.defined over all non~negative integers k:

8 (k) = 1

m k-m

=8

if 0 ;5; k s om,

if m s k s 00. (8-6)

Then, in terms of this em(k), \ is defined as

5 • = e (k)f (~)( T.)afbk-i

k m i~O 1 k-l

= em(k)bk(~)F(-L,-k;-T-k+l;~),

where F(i,j;k;x) or 2Fl(i,j;k;x) is the Gauss hyptergeometric series

(Abramowitz and Stegun, 1964):

163

(B-7)
00 (i)n(j)n F(i ,j ;k;x) = n=O (kJn

n

x

nr· (B-8 )

For negative i orj, the Gauss series reduces to a polynomial. This makes the

evaluation of equation (B-7) a finite task.

B.2. Numerical Results

Blocking probability P has been computed for several values of param- m

eters m, 8, L, T, a and b, using the,exact solution as given in equations

(B-5) to (B-8). A sample of the computations is shown in Figure B-1. The

figure plots Pm (fraction of time) versus the initial offered load, La+Tb.

To transform the x-axis into the slightly lower values of the lIeffective

offered 10ad,'1 one has to carry out the modifications indicated in Appendix A.

The exact points of Figure B-1 apply to rather modest parameter values;

namely, to m=5, 8=0, L=50, T=lO~ and b=.l. The load per line, a, is varied

to achieve the range Gf initial loads plotted. The range of Pm values is

purposely kept around the 1% level because that appears to be of practical

interest to access area applications. Since the evaluation of even such

simple points turns out to be quite time consuming, other quicker methods of

finding Pm must be of interest..

The two approaches taken here involve bounds and approximations. For

an upper bound on P , one may take for all 0~8s1 the Erlang Band C hybrid m

(Nesenbergs, 1979):

B(m,La+Tb)C(m,La+Tb)

Pm S 8B{m~La+Tb)+(l-e)C{m,La+Tb) · (8-9 )

This bound is particularly easily evaluated with the available Erlang B

tables (AT&T, 1961; Siemens, 1970), if written in an asymmetric way,

1 8 . l~(la+Tb) Pm ;::: iil(La+Tb) + B(m,La+Tb) · (B-10)

Note, that for 8=0, one always ha~ PmsB(m,La+Tb).

This upper bound on the previously computed true values is shown in

Figure B-2. The upper bound appears to,be nearly 50% above the exact points

for this case. It seems toounprecise for approximati6n p~rposes.

164
IO-I.----------------~----~---~-----,

Q)

E

..-=

"I0

c:: 10-2

0

:;:

u

e

LL

p...E

m = 5

e = 0

L = 50

T = 10

b = 0.1

1.4 1.6 1.8 2.0

La + Tb [Erlangs]

1.2

-3 10 I'--.O---------l'------....a..----~----.-..-------"-----

Figure B-1. Probability of blocking PL11 (based on fraction of time) versus the initial load, La+Tb, for parameter values indicated. .

165
10- 1r-------,....__----r-------r-~--_,__-o---_._,r__---__,

2.0

m = 5

e =0

L = 50

T = 10

b = 0.1

1.4 1.6 1.8

C La + tb [Erlangs]

1.2

IO-3"--_--...,.jL...-~ ............__--~------...-.---L-------I'--------'

1.0

Figure B-2. Bounds on probabtl ity of blocking ~. (based on fraction of

time) versuS the initial load, La+ID, for parameter val~es indicated.

166
Figure B-2 also depicts a lower bound on Pm. The lower bound is again

off by same 50%. It happens to be based on the formul a

where in the ·nearest integer sense

I :: mLa/(La+Tb),

J :: mTb/(La+Tb).

(B-1l)

(8-12)

An approximate value for Pm could be derived from averaging the two

bounds (Fig. B-2) in any of several possible ways. This, howevertis not

the approach taken here. In what follows, one uses the approximation

Pm Ao(1+a1e+a2e2)~ (B-13)

where

1(L-J T-J ) Ct1 = "2 1+1 a + ·J+l b , (B-14 )

When efs negligibly small, the approxtmattonIjl-l S) reduces to e=2.7l8

times the previous lower bound [see (B-ll) and Fig. B-2]. The fit of the

approximation to the exact values is illustrated in Figure B-3. In the

1% neighborhood for P,m one expects this -approximation ..to be within a +10%

relative error range.

Approximatinn (B-13) has been used to compute Pm f?rvariql)s service

facility configurations. For initial loads ranging f'rom 2 to IuErlanqs ,

and for 8=0,1/2,1, this is shown in Figure 8-4. Figure 8-4 again plots

probability of .blocking, Pm' versus the number of servers m.The range of

P is restricted to a relatively short and linear region from .5% to 2%. m >

As seen, the effect of the hybrid loss-delay para~eter a becomes increasingly

noticeable only as the load a~d the number of servers increase.

The loci at which Pm assumes a selected constant value, such as 1%,

can be readily interpolated from Figure B-4~ ~hen this is done for

167
10-I ,.------.-----,..-------,.-----r-----,---------.

(1)

E

'0

c: 10-2

0

+=0

e

IJ..

~E

m = 5

e = 0

L = 50

T = 10

b = 0.1

IA I~ 1.8 2.0

La + Tb [Erlangs]

1.2

10-3'--- --J.- ...J....- ---L ...L... --JL.- -J

1.0

Figure B-3. Approximation of blocking probability P (based on fraction

of time) versus the initial load, La+Tb~ for parameter

values indicated.

168
12

_.e : 1

-,_.--'

- 2 _ _"._1: 0

, a", , , I

8 9 10 II

m [No. of Server~

1

a =0.04

La +Tb=4

6

1

%

, 201 ice c, C _. , c c , • /0' iii i

0.50/0' , I.' ,

5

Pm

0'\

sc

Figure B-4. Blocking probability approximations for various initial loads, La+Tb,versus the

number of servers m. For L=50, T=lO and b=5a.
sufficiently Iarqenumber of loads, a's' well as for the correspondtnq choices

of numbers ,of servers, the cUrves of Figure 45 (main text) materialize.

B.3.R'eferences

Abramowitz, M., andI.A. Stegun, Eds. (1964), Handbook of Mathematical

'Functions, National 'Bureau 'of Standards, AppltedNath, Series (55),

Washington, DC.

AT&T (1961), Switching Systems, American T'elephone and Telegraph Co.,

New York, 'NY.

Cooper, R.B. (1972), Introduction to Qu~uein9 Theory (MacMillan Co.,

New York, 'NY) •

Kleinrock, L. (1975), Queu:elng Systems,'Volume I: Theory (John Wi'ley and

Sons, New York, NY).

Nesenbergs,M. (1'979),' A ','hybrid of ErlangB and C formulas and its applications, IEEE Trans. on comm., COM-27, January, pp. 59-68.

Siemens (1970) , Telephone Traff;ic Theory Tables and Charts (Siemens AG,

Munchen, Germany).

,170
APPENDIX C. THREE KINDS OF CALLS AT A LINE/TRti~k~~tttH

e.l. Assumptions

In this section, the problem of three kinds of calls through a switching

network is "examined further. This is the same problem tHat was introduced

in Section 5.4 of the main 'text. An illustration of the'moael is given in

Figure 46. One assumes:

o Blocked:calls-arelost (cleareq).

o Arrivals are generated by three independent PoissdH pf8tE!$ses. The

i nterarriva1 times are exponent; al.

o The service or holding times are exponentially distritiutedwiththe

same unity mean for all.

o The number of ltnes (L)andtrunks (T) are given con's:iahts.

o All three-service 'requests come frominfi'nite user rj'(jptila'tions.

o The switching network isnonblocking~

o The s,wi tchi ng network pravides full, avat1abt1i ty,

o The offered loads (arrival rates) are different for· the three service

classes.

To be more specific, assume the notation-summarized in Table C-l. When'

local calls, d distant calls, and t tandem calls are in progress, one says

that the system is in state (R"d,t). Individual states may Occur with

different frequencies. Only states with min(R"d,t)~O and rnax{2R,+d:..L,d+2t-T)sO

can ever occur. As before, the steady state or equt1; brium probabi 1; ty of a'

state (l,d,t) shall be denoted by p{t,dtt). Impossible ~tatej (t,d,t) will

have p(l,d,t)=O by definition. Selected sets of p(R"d,t»O tdntribute to

the. three sought blocking probabt l tttes r Pi for local cails, Pd for distant

calls, and P

t for tandem ~alls.

, ,. ,

TableC-l. Summary and Notation for the Three KindsoT Traffic

Kind of State Probe of Offered U$ed Number of

Call Index "Blocking Load lines Trun-ks

Local R, P£ A 2 0

Distant d Pd B 1 1 ~::

Tandem t Pt C 2 rc~... > 'J"

171
Let the offered loads be A, B, and C Erlangs for the local, distant,

and tandem calls, respectively. Finally, note that a local call cannot be

completed unless th~re are at least two idle lines available. Likewise, a

distant call demands at least nne idle line plus one idle trunk. A tandem

call needs two trunks. Otherwise blocking occurs. Table C-2 lists all

thebloc.king eventualities as a function of the state descriptors> (2,d,tJ.

For example, if 22+d=L-l and d+2t=T-l~ ~hen only local and tandem calls are

blocked. An additional distant call may still be accepted. In the lower

right corner of each cell there is a number i=1,2, ... ,9. This number is

used solely for indexing or subscripting~ For our previous example. of

22+d=L-l and d+2t=T-l, i=5.

Table C-2. Occurrence of Local, Distant, and Tandem Call Blocking

as a Function of State Index Set (2,d,t)

d+2t=T d+2t=T-1 d+2t~T-2

22+d=L Local Local Local

Distant Distant Distant

Tandem 1 Tandem 2 -- 4

22+d=L-l Local Local Local

Distant -- -- Tandem 3 Tandem 5 -- -_. 7

22+d~L-2 -- -- -- Distant -- -- Tandem 6 Tandem 8 -- 9

C.2. Equilibrium Equations

This section constructs the equilibrium equations for the unknown

three-dimensional state probabilities p(~,d,t),where 2,d,t=O,1,2, ...

Previously, similar identities were called steady-state flow conservation

laws or 1I0UT=IN II equations [see (A-2), (A-5), and (B-1 )J. In this problem,

there is sufficient additional complexity to warrant a formal attempt at

simplification.

To start, note the normalization property

I p(2,d,t) = 1.

all 2,d,t

172

(C-l)
Also note, as pointed out earlier, that p(£,d,t} must vanish whenever either

min(£,d,t)<O or when max(2£+d-L,d+2t-T»O.

In what follows, the equilibrium equations will be written in the form

of vanishing vector products,

e = O. (C-2)

Here, the dot (e) denotes the ordinary inner product of two seven-dimensional

vectors. The vector V will always be a column (vertical) vector,

p(£,d,t)

p(.Q,-l,d,t)

p(£,d-l,t)

V = p{£,d,t:l) (C-3)

p(£+l,d,t)

p(£,d+l,t)

p(Sl"d,t+l)

It represents the unknowns in this problem.

The will be a row (horizontal) vector, also with s~ven elements.

Depending.on system states, vector will take various forms. These forms

are introduced next with the aid of constituent vectors ~i' i=1,2, ... ,5:

~1 == [1 , 0 , 0 , 0 , 0 , 0 , OJ,

R2 = [~+d+t, -A, -B, -C, 0, 0 , OJ,

.!l3 = [0 , 0 , 0 , 0 , -{~+l}, 0 , OJ, (C-4)

14 = [0 , 0 , 0 , 0 , 0 , -(d+1), OJ,

!!s = [0 , a ,0 ,0 , 0,0 , -(t+l)].

Next, for each of the nine state ~ategories of Table C-2, the row

vector H.(j=1, ... ,9) is constructed as follows: -J

!il = .!i2 = !!3 = !l2'

14 = C!!l + !!2'

.!is = B.t!., + .t!.2 + 14,

::: A!!, + .t!.2 + !!3' (C-S)

!!7 = {B+C)R1 + !!e + 14 + ~,

= {A+B)~l + !!e + ~3 + 14,

Hg = {A+B+C )~1 + !!e + ~3 + 14 + !!s.

Returning to (C-2), one now asserts that

H. e V = 0, j = l , ... ,9, (C-6 ) -J

173
represents the equilibrium equation for the state j, as indexed in each cell

of Table A-2.

For instance, when 2~+d=L-l and d+2t=T-l hold, one has j=5. For this

case ~.V=O boils down to

(B+~+d+t)p(~,d,t) - Ap(~-l,d,t) - Bp(~,d-l,t)

- Cp(i,d,t-l) - (d+l)p(~,d+l,t) = o. (C-7)

The complete equation set to be solved consists of (C-3) to (C-6).

One finds Table C-2 helpful to verify that no terms are overlooked in this

complex construction.

Assume that T~L and that both T and L are even. Then the number of

unknowns, which is the same as the number of equations, can be found. For

each d in the set, d=0,1,2, ... , T/2, the summation over all- possible and

t is relattvely simple. The resultant number of unknowns equals

2

T:2[T(T;1 + L

2T} + L:2J == L~ . (C-8)

For a modestly sized switching facility, such as given by L=140 and

T=24, the number of equations (same as the number of unknowns) amounts to

roughly 10,000.

C.3. The Formal Solution

Given the above problem of considerable complexity, it seems rather

fortunate that a solution can be constructed by a simple method. That

method is the same separability device or product method (Cooper, 1972)

employed in Appendix B [see, fo~ instance, equations (B-2) and (B-3)].

Assume

tc-s)

Then the equilibrium equations (C-6) break down to separate equations for

Pl(~)' P2(d), and P3(t) that can be solved by inspection. The result is

AiBdCt

p(~,d,t) = p(O,O,O) ~!d!t! ' (C-10)

where

[

Ai BjCk]-l

p(O,O,O} = I "'"'kl " all i ,j , k 1.J. ·

174

(C-ll)
(C-12)

It is beyond the scope of this short appendix to prove that every

condition is satisfied by this solution. However, a short example may

suffice.

Consider (C-6) for j=9. With the aid of (C-3), (C-4), (C-5) and (C-9),

this reduces to

[(A+l)Pl(l) - AP1(1-1) - (1+1)Pl(1+1)]/Pl(1)

+ [(B+d)P2(d) - BP2(d-l) - (d+l)P2(d+l)]/P2(d)

+ [(C+t)P3(t) - CP3(t-l) - (t+l)P3(t+l)]/P3(t) = O.

Clearly, if all the square brackets vanish, one has a solution. But the

expressions in the square brackets are akin to those that occur for the lost

calls held, or the MJM/oo, model that is known to result in the Poisson

formula (Riordan, 1962; Kleinrock, 1975; Bear, 1976). Thus

Pl(~) = Pl(O)A1/1J,

P2(d) = P2(O)Bd/dl, (C-13)

p

3(t) = P3(O)C

t/tJ.

This formal solution is likewise valid for all other j=1, ... ,8. The constant

in (C-9)- is easily determined with the help of the normalization (C-l).

It leads to the p(O,O,O) expression given in (C-ll).

The blocking probabilities P

1, P

d and Pt (see Tables C-l and C-2) are

sums of p(~,d,t)'s over appropriate (~,d,t) sets. For example, the index

set for local call blocking is (1,2,3,4,5,7). For distant calls blocking

occurs over (1,2,3,4,6), and for tandem calls ~n (1,2,3,5,6,8). Their

numerical evaluation seems to call for thorough planning, followed by

extensive use of computing machines.

C.4. References

Bear, D. (1976), Principles of Telecommunication - Traffic Engineering

(P. Peregrinus Ltd., on behalf of lEE, Telecomm. Series 2,

Stevenage, England).

Cooper, R.B. (1972), Introduction to Queueing Theory (MacMillan Co.,

New York, NY).

175
KleinrockJ L. (1975J. ~ueueing Systems. Volume!: . Theory (John Wiley and

Sons, New York,NY).

Riordan, J. (1962), Stocastic Service Systems (John Wiley and Sons,

New York,NY).

176
FORM OT-29

(3-73)

u.s. DEPARTMENT OF COMMERCE

OFFICE OF TELECOMMUNICATIONS

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION OR REPORT NO.2. Gov't Accession No.3. Recipient's Accession No.

NTIA ~eport 79-26

4. TITLE AND SUBTITLE

SWITCH ELEMENT CAPACITIES IN ACCESS AREA DIGITAL

SWITCHING SYSTEMS

s. Publication Date

September 1979

6. Performing Organization Code

ITS

7. AUTHOR(S) 9. Project/Task/Work Unit No.

R.F. Linfield and M. Nesenbergs

8. PERFORMING ORGANIZATION NAME AND ADDRESS

U.S. Department of Commerce

National Telecommunications & Information Administration 10. Contract/Grant No.

Institute for Telecommunication Sciences

325 Broadway, Boulder, CO 80303

11. Sponsoring Organization Name and Address 12. Type of Report and Period Covered

U.S. Army Communications Systems Agency

ATTN: CCM-RD

Ft. ~1onmouth, NJ 07703 13.

14. SUPPLEMENTARY NOTES

1S. ABSTRACT (A 200-word or less factual summary of most si~nificant information. If document includes a significant

bibliography of literature survey, mention it here.)

The capacity of a digital circuit switching system is defined in terms of its four

major elements: the traffic offered by the interface element, the maximum traffic

carried by the switch matrix, the maximum number of call attempts handled by the

control processor, and the maximum number of calls handled by the signaling elements. These element capacities may be engineered for the expected traffic

(e.g., call attempts and holding times), the performance objectives (e.g., blocking

probabilities and tolerable delays), the processor capabilities (e.g., speeds,

memory sizes,service features), and the signaling techniques (e.g., common channel

or per-channel signaling).

In a properly engineered system, the interrelations between the capacity of all

elements should be considered. This report discusses such interrelationships and

characteri zes representati ve swi tch configurati ons on the basis of the four major elements. The results obtained have applications in developing non-tactical network~

for military access areas where the communications profile is known. This is

16. Key Words (Alphabetical order, separated by semicolons) demonstrated for Ft. Monmouth and 1 ts

environs. Estimates of traffic statist lcs

and switching requirements are made with

the aid of available Ft. Monmouth terminal

density profiles.

17. AVAILABILITY STATEMENT

[Xl UNLIMITED.

o FOR OFFICIAL DISTRIBUTION.

*u. S. GOVERNMENT PRINTING OFFICE 1979 - 681-676/105 Reg 8

18. Securi ty Class (This report)

Unclassified

19. Security Class (This page)

Unclassified

20. Number of pages

192

21. Price:

L'SCOMM-DC 29716-P73