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ARI Research Note 86-96

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INFORMATION STORAGE AND ACCESS

IN DECISIONMAKING ORGANIZATIONS

Ghassan J. Bejjanl

Morgan Stanley

and

Alexander H. Levis

Massachusetts Institute of Technology

for

Contracting Officer's Representative

George H. Lawrence

BASIC RESEARCH LABORATORY

Milton R. Katz, Director

DTIC

JAN 2 71987

n $ a

U. S. Army

Research Institute for the Behavioral and Social Sciences

November 1986

Approved for public rtltatt; distribution unlimited.

87 1 21 10
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U. S. ARMY RESEARCH INSTITUTE

FOR THE BEHAVIORAL AND SOCIAL SCIENCES

A Field Operating Agency under the Jurisdiction of the

Deputy Chief of Staff for Personnel

WM. DARRYL HENDERSON

EDGAR M. JOHNSON JJ01"

W

JTcchnid Director Cwnn-nding

Research accomplished under contract

for the Department of the Army

Massachusetts Institute of Technology

Technical review by

Steve Kronheim

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REPORT DOCUMENTATION PAGE

1. RtPORT NUMICK

ARI Research Note 86-96

2. OOVT ACCESSION NO

4. TITLE (m* Suhiltl»)

INFORMATION STORAGE AND ACCESS

IN DECISIONMAKING ORGANIZATIONS

». AuTHORfaJ

Ghassan J. Bajjanl and Alexander H. Levls

I. PKRPORMINO ORGANIZATION NAME AND ADDRESS

Laboratory for Information and Decision Systems

Massachusetts Institute of Technology

Cambridge, Massachusetts 02139

II. CONTROLLING OFFICE NAME AND ADDRESS

U.S. Army Research Institute for the Behavioral

and Social Sciences, 5001 Eisenhower Avenue,

Alexandria, Virginia 22333-5600

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READ INSTRUCTIONS

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MDA 903-83-C-0196

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2Q161102B74F

12. REPORT DATE

November 1986

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29

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14. SUPPLEMENTARY NOTES

George H. Lawrence, contracting officer's representative

This research partially funded by Office of Nava- Research

i Availability

IS. KEY WORDS (Ceollnue en reveree »Ide II neceeeery mtd Identity by ftlec* number;

Decisionmaking Database

Organizational Structures Evaluation

Organization Performance Workload

Dlst

A-(

Cedes

Avail arli/vT

SpecieL

20. ABSTRACT (Cm**ue am referee et* H rmc—eetr md Identltr by Meek nunber;

Information storage and access in decisionmaking organizations is modelled using a Petri Net representation. A centralized and a decentralized database configuration are analyzed, and their impacts on the decisionmakers' workload are

assessed. Organizational protocols are defined, and their criteria of acceptability presented. Protocols' key variables, minimum allowable input interarrival time, and response time are determined for two organizational structures

- parallel and hierarchical. A numerical example suggests the use of timeliness

(over)

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ARI Research Note 86-96

20 ABSTRACT (continued)

as a third organizational attribute - the first two being workload and

performance. It also demonstrates the importance of updating coordination

in evaluating the organization's performance.

UNCLASSIFIED^

11 MCURITV CLASSiriCATtON Or TNM ^ACCrWhm Dim Bnffl)

mmma^ammmmma*mmm^mmm*^^^*m*M.ivii*M.mLiJki\jM\Jiiuk, _p.( _J»rj»r"_» rVM p^ '■■ * r^» n mm tau — n »h ia M n n rv*«».n.« r ^ftjiKJ^Kl^H^HMHH
INFORMATION STORAGE AND ACCESS IN DECISIONMAKING ORGANIZATIONS

by

Ghaasan J. BeJJani

••

Alexander H. Levia

•••

\

ABSTRACT

Information storage and access In decislonmaklng organizations Is

modelled using a Petrl Net representation. A centralized and a decentralized database configuration are analyzed, and their impacts on the

declslonmakers' workload are assessed. Organizational protocols are

defined, and their criteria of acceptability presented. Protocols1key

variables, minimum allowable input interarrival time, and response time

are determined for two organizational structures: parallel and hierarchical. A numerical example suggests the use of timeliness as a third

organizational attribute - the first two being workload and performance.

It also demonstrates the importance of updating coordination in evaluating the organization's performance.

•This worlc was carried out at the KIT Laboratory for Information and

Decision Systems with support provided In part by the Office of Naval

Research under Contracts NOO014-83-K-O185 (NR 274-349) and N00014-84-K-0519

(NR 649-003) and In part by the OS Army Research Institute for the

Behavioral and Social Sciences under Contract No. MDA903-83-C-0196.

••

Morgan Stanley, 35 Water Street. New York. NY 10041

•••Laboratory for Information and Decision Systems. MIT. Cambridge,

MA 02139.

tw>^M^mmmmmmmmamamt\.-h 'A it L-W w uvv.vv% .v L-V WV Livukr-v LV v» L-W < t'JiL% VJW\IW\»AAI\*.L^> V\I. VNTJWV*
1. IMTRODOCnON

During th« past d«oad«, infm-aatlon theory has b*ea appllad to the

analysis and valuation of organisations. rlrst dovslopod by Shannon

(Shannon and Vaarar. 1949), information theory aaturad into a aathaaatioal

thaory in its own right, and was applied to the study of various

ooMunioations systeas (Gallager. 1968). It was then used ss a basic tool

for aodeling huaan deoisionasking (see Sheridan and Parrel, 1974, and

Drenick, 197S). The Partition Law of Znforaation (Conant, 1976) provided a

physical interpretation of the aathaaatioal expressions derived by using

the n-diaensionsl version of the theory.

A two-stage inforaation theoretic aodel of the deoisionsaker was

introduced by Boettcher and Levia (1912). Quantitative aeans for aeasuring

the huaan deoiaionaakers' workload and the organization's perforaanoe were

designed under a set of restrictive assuaptions. Subsequent research

effort (Hall and Levis, 1994} Chyen and Levis, 1985} Toaovlc and Levia,

1984) was oriented towards relaxing some of those assuaptions and resolving

acre ooaplex issues related to a realistic use of the deeisionaaking aodel.

This paper addresses the issue that deoiaionaakers are not aeaoryless

(an aasuaption in the original aodel) and that inforaation storage and

acccess devices are actually put to service in aost aodern organisationa.

The study of databaaes in aoyolioal organisationa la approohed along two

directions: (a) computation of modified activity terms that represent the

decisionaaker'a workload and (b) consideration of time and delays in the

normal functioning of an organization. The two directions are developed

aeparately but are brought together in the illustrative example of the

last section.

Pigure 1 shows the Petri Net representation (Tabak and Levis, 1984) of

the two-stage aodel of the n

tb member of an organization. His input xn

is

a component of a single vector source distributed by a set of partitioning

aatrioea aaong all the deoiaionaakers (Stabile and Levis, 1984). The

dedaionaaker processes this input in the situation sssessaent (SAn) stage

1\A.njA**UfcMBl*^UW\fc\«^WUW\Ä^^

1A UV».VIT«Irt*U> UVV> w> .> V-HIJ
X

-OH

L^

Figur« 1. Petri Net Representation of the n

th Declslonmaker of the

Organization

to cetei^lne or »elect a particular yalue of the rarlable z

11 th»t denotes

the situation. Be may cooDunlcate his assessment of the situation to other

embers (zn0) and be may receive their assessments In return (zon). This

supplementary Information may be used to modify his assessment. I.e.. It

may lead to a different value of z

n

denoted by z

n

'. Possible alternatives

of action are evaluated In the response selection (RSn) stage. The outcome

of this process Is the selection of a local action or decision y

11 that may

be oonnunlcated to other team members or may form all or part of the

organization's response. A command Input from other dedslonmakers. v .

may affect the selection process.

The situation assessment stage consists of U algorithms (fj.

1-1.....0). The value taken by the variable u

n

determines the algorithm to

ÄiamiüOüL>jflba*5U>jouo^jO'^^ ..•c.vfr^jvcnuwwAu, yiüi^VNiMj^wuAva
wmmmi^mwrwi i ii w^n^mmmmrvwm

b« used, and is obosan according to the probability distribution p(un).

SiBilarly. the choice of an algorithm in the RS stage is determined by the

variable t

11, with probability distribution pC^lz0

').

As a response to the need for aemory and information handling In

today's organizations, the oonoept of Deoision Aids first appeared a 11tie

ore than a decade ago. These devices are evolving into well-integrated

Decision Support Systems (DSS) (Keen. 1981). The database is one of the

three main parts of a Decision Support System. The other two are an

information management program, and a machine-user interface (computer

terminal) (Sprague, 1980} Sprague and Carlson, 1982). This paper will

address the database and decisionmaker/machine interface Issues from an

Information theoretic point of view. The database's storage and access

procedures, and their Impact on the decisionmaker'a workload and

performance levels, will be described.

2. THE GENERAL DATABASE MODEL

The database model developed in this paper conforms to the traditional

definition of an information storage device: it can receive Information

from an external source, it stores it adequately, and it delivers this

information, or part of it. whenever accessed by its users. The Petri Net

model adopted here consists of two stages (see Fig. 2). The first stage,

transition C, receives an input from the decisionmaker who requests access

to the data. This input represents the situation in which the user is.

Transition C determines then the nature of the Information needed to cope

with that situation, and sends a query to the next stage, D. Transition D

performs the actual search, and delivers the data to the decisionmaker at a

predetermined stage of his internal decisionmaking process.

Figure 2. Petri Net Representation of the General Database Model

iv\>v^*vv\v^>:^v:.x>>:w>j.>u,%jMii^M^>jfl^^^
Databases oan be used In «Itbar a oeotrallzed or a daoentrallzed

configuration. Daoentrallzed databases are defined here as Individual

storage units, aooessed ezolusively by one declslonnaker. and holding and

deliTerlog inforaation relevant to this deolsionaaker'a task only. It was

proved (Bejjani, 198S) that the Increase in activity due to a centralized

or decentralized configuration were siallar. However, there are Important

differences. First, the time associated with the query process Is auch

shorter when the database is an individual one than when it is centralized.

In effect, in the former oase, no Irrelevant Information is to be scanned

and then discarded, which happens in the latter oase, and the system's

answer to its stimuli is more timely. However, an advantage of a

centralized database structure Is that It allows for more convenient

updating. It oan be updated in one operation, providing all the

dedsionmakers with equally recent information, whereas decentralized

databases require a much greater updating effort to obtain the same result.

This paper will develop information theoretic aspects of the centralized

databases and discuss the decentralized oase briefly (for a comprehensive

comparison of the two configurations, tbe reader is referred to BeJJanl,

198S).

2.1 Centralized Databases

A centralized database is a database shared by all members of the

organization. It is physically located in one place, and individual

terminals allow the dedsionmakers to access It independently. In the

Petri Net representation, a centralized database is modeled as one unit,

comprising several transition C/transition D sequences. There are two such

databases, one for the SA stege, called DBSA. and one for the HS stage.

DBRS. Tbe inputs to transition 0° in DBSA are the inputs to the arh

decisionmaker. x

0

, and the variable u

11 indicating the SA algorithm he Is

about to use (see Fig. 3). Transition C

n

emits then a message towards

transition 0° that carries a query for the information needed for DMnto

process z

0

through the selected SA algorithm. D

n

in turn delivers the

requested data, d|A. to the decisionmaker. who receives It as an input to

the algorithm he is using. The usage of DBRS follows a similar rationale

applied to the RS stage.

LlAMMhfiKQiK
Y

l-o

Figure 3. Petri Net Representation of DM0Using Centralized Databases

The use of databases has a significant impact on the decisionnaker's

workload, as can be seen In the following development. Activity rate terns

are derived by applying the Partition Law of Information Rates (Conant,

1976) to the deolslonmaklog model ured here. For a more complete

description of the calculations, the reader is referred to Bejjani (198S).

The modifications to the basic model are due to the presence of tno

supplementary variables. d|A and d§s, and to their relationship with the

existing structure. For simplicity, the superscript n will be omitted in

the following equations whenever confusion may not arise.

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Throughput Hat«:

Ft- fU.d^.^.T^.d^u.z00.!.f.yno.y) ttl

Blookag« Rat«:

rb - i(i,^..<».T"',dlls) - rt <»

Itela« Hat«:

F - H(u) H_(T) (3)

n T

Coordination Hat«;

0

Fc- } (|J(p(x.d3A))*^:H(pi))+H(z)

i-1 SA

*lt (p(z.zon)) *lj (p(I.y0n))

o o

T

S3

H(z) H(2) + H(I.?) fx(x,dSA:zon) + Ts(x.dSi.zon:v

0n)

* ^.»(x.^.«00."

0

"'-») ">

wh«r«

p1- p(u-i) ; p. - p(v-J) (5)

MttftdiuuftflBttyaAffifi^^
(p) plog>p (l-p)log1(l-p) (6)

and oi la tha nuaber of Tariablaa of the algorlttaa 1 that ara reinitialized

at each iteration. The ayabol T^ designates the mean Intararrlval tiae of

the Input to the SI stage. TRS has an equivalent aeaning with respect to

the HS stage. The aean Input interarrival tiae can be used In the

equations» If the interarrival tiae la not constant, by regulating the

source (Hall, 1982). The functions |£. gjj"^, gj and jj are the individual

coordination rate functions of the Si, A, B, and RS algorithms, and are of

the following fora:

«i 5

5

u *ty -

i

u

(wi) (7)

The terms H(z), H(Z), H(S,?) in (4) can be interpreted to represent

the direct coordination rate between aubsysteas, through the faot that one

subsystem's output is another's input. However, indirect coordination

between the subsystems is accounted for by the transmission rate terms.

f2(x,dSA:2

on) represents the coordination rate that la due to the

relationship between x and dSA, and z

on

. Indeed, if tha Inputs to OH0and

those to the rest of the organization (BO) are related, or If d|A and d^,

m J

1 n, are not totally independent, due to the structure of the storage or

the updating process in the centralized database, then z

on can bring to S

information about the inputs to the system that is not oootained in z.

Similar interpretations hold for the other two transmission rate terms.

The term T2,^(x,2on,dSA,v

on

:dRS) raises the question of the relationship

between dSA and dHS, i.e., whether the situation assessment database (DBSA)

and the response selection one (DBBS) are related.

2.2 Decentralized Databases

A decentralized database structure is shown in Figure 4. The only

difference with respect to Figure 3 is the presence of only one transition

(^/transition D

n

sequence per database, which aodels the exclusive use of

hÄ"^M>fr&^^
Y

HD

Figure 4. Petri Net Representation of DM0Oaing Decentralized Databases

each database by a single declsionmaker. Apart from that, decentralized

databases are assuoed to function in exactly the same manner as centralized

ones.

2.3 Plzed Databases and the Memoryless Model

The results in section 2.1 were derived assuming the data dSA and d^

to be variable quantities. However, it might very well be the case that

dSA and d^ are fixed, either because the databases are never updated or

because the values taken by dSA and d^ remain valid during a very long

time, compared to the mean input interarrival time. In this simple case,

the database's direct contribution to the dcdsionmaker's activity rate is

null, and the expressions developed above become similar to those derived

in the basic memoryless declsionmaker case. They are derived by simply

eliminating the variables dSA and dj^ and the input variables to the

c^&^^mmma^
databases from the equations, whlob shows that the reduction fron the

database-equipped aodel to the aeaoryless one Is consistent.

3. PROTOCOLS AMD THEIR APPLICATION TO ORGANIZATIONAL STRUCTURES

3.1 Definition of Protocols and Determination of Their Key Tarlables

A protocol Is the description of the chronological order In which

elementary tasks have to be performed within one dedslonmaker as well

ss between two or more of them. Determination of procotols Is a

fundamental design problem for organizations In general* and of updatable

database-equipped ones In particular. Indeed, If the sequences of

operations for each dedslonmaker are not clearly defined, and If the

updating tempo of the database does not take these sequences Into account,

chaos can result. In brief, the situation could arise where different

declslonmakers would be accessing different databases at different times,

with different levels of accuracy and relevance of the data. In order to

process the same Input.

Since the Petrl Net representation (Tabak and Levls, 1984) clearly

Illustrates the organization's protocol as defined above and since a key

notion In the definition of a protocol Is the amount of time Involved at

each step of the dedslonmaklng process, an acceptable protocol for a given

organization will consist of Its Petrl Net representation supplemented with

the allocation of a processing time to each transition. The processing

time In fact represents the maximum allowable duration of a transition for

the orgadzatlon to function In an orderly fasdon, following Its operating

protocol.

Assumptions: In devising an acceptable protocol for the kind of

orgadzatlons dealt with here, the following assumptions are made:

(1) - the source emits the Input Z with a constant Interarrlval time

(2) - the various transitions have constant processing times.

(3) - ooHBunlcatlon between transitions Is Instantaneous.

10

^to&toM^^ «fvr.vX ^^m^^SbÄ^M
(4) - any transition can process an Inoomlog input as soon as it has

finished processing the previous on«* and no sooner.

(5) -no queusing is allowed at any stags of the process.

Assumptions (1) and (2) are a corollary of the broader assumptions

that the whole systea operates in stsady state. Assumption (3) states in

faot that all the dsoisionaakiog occurs within the transitions, and that no

processing time is allooated to places. Assumption (4) is putting the

"pipe-line effect* into words t this assures that the information flow

through the system is continuous. Assumption (S) is a prerequisite to the

application of Patri Met theory to the study of information theoretic

deoisionmaking aodels: in effect, when queueing takes place, two or more

different tokens can coexist in the same place. Since transitions do not

have any means of recognizing priorities in choosing one token as an input

out of the same place, the queue cannot be managed, and the organization's

protocol is transgressed. (For a relaxation of this assumption, see Jin,

198S).

Proposition: Under assumptions (1) to (S), two necessary conditions

for an organization's protocol to be acceptable are:

every transition in the system must have a processing time smaller

than or equal to the mean Input interarrival time.

- the total amount of time spent by a token in one place cannot exceed

the mean input interarrival time.

Both necessary conditions provide a symmetric analytical tool.

Indeed, if the processing times of the transitions in the system are fixed,

then the minimum admissible input interarrival time for the organization

can be determined: It is equal to the greater of two quantities: the

maximum processing time present on the Petri net diagram of that

organization, and the maximum time any token spends in any place.

Determining this minimum interarrival time is a very useful way of

comparing the effectiveness of different organizational structures in a

given oontext.

The second necessary condition applies in oases of organizational

11

a>:^>v:::v:;;>:<>-
Interactions wb«re on« doolslonaaker sonda aoae information to anottaar and

cannot proceed before receiving a message back. Thus, the proposition

provides a way of determining the upper limit of tbe response time of this

otber decisionmaker, everything else being fixed. This will be made

clearer in tbe next section.

As a last comment, one sbould realize that tbe use of tbe proposition

is not restricted to decisionmaking organizations. In fact, its argumeota

are relevant to any acyclical information processing structure where

Assumptions (1) to (5) are satisfied«

3.2 Construction of Protoools for tbe Centralized Case

In this section, tbe proposition will be used to develop protoools for

two particular organizations using a centralized database configuration.

Tbe basic quintity for each organization is f« tbe processing time of any

SA or RS transition. It is assumed to be identical for all such

transitions in both organizations, and it will be the unif used for all

quantities computed here. Furthermore, T is assumed to be greater than the

processing time of other types of transitions* on the grounds that more

decisionmaking takes plaoe in SA and BS transitions than in the others.

Tbe database's response time is assumed to be T as well.

Parallel Organizational Structure

In a parallel organizational structure, decisionmakers «re linked by

somewhat symmetrical relationships: they do not formally Issue commands to

each otber, and they can share information at all stages according to preestablished operating procedures. The parallel structure considered in

this work is a three-person organization. (Fig. S) called "Organization P"

from here on. DM1and DM* use only one SA algorithm and two RS algorithms

each, and DM* has tbe choice between two SA algorithms, whose output can be

processed by only one RS algorithm. The command input v

on is absent from

tbe model, due to the non-hierarchioal structure; the decisionmakers do

however share information about their situation assessments.

12

a^Mam^^maMMiaMaMffl^^
Organization P uaes two oantrallzad databases. DBSA and DBRS; An

acceptable protocol for this organisation has been darlvsd and is given in

Figure S. Its sain characteristics are the ainlaua interarrlval time (IT)

it allows, T, and the organization's total response tine (RT), the tine

Interval between the arrival of the input and the generation of a

corresponding response* which is equal to 19T/3.

Figure S. Protocol of Organization P Using Centralized Databases

13

<iÄ&&^^
Hitrarohieal Organization Structur«

A hlararotaloal organisational struoture allows daclslonaakera to hava

an Influance on «ach othe."'s response selection. This Influence can be

represented by a command Input. v

on

. The hierarchical structure analyzed

here Is a three-person organization, known as organization H, equipped with

centralized databases as shown In Figure 6.

Figure 6. Protocol of Organization H Using Centralized Databases

14

^t^^^^^^
Organization H oonslsts of two declslonoakers who aotually contribute

to Its output. DM1and ON*, and on« coordinating deolslonaaktr, DM*, who

analTiaa DM1'» and DM*'a situation assossaants in order to Issue a coonand

to than that carries bis instructions about the way the organization's

response should be constructed. DM* is not in contact with the

environaent, therefore he does not need an SA a tage, neither do DM* and DM*

need an information fusion transition. A. The three deoisionmakers In

organization H bays each two HS algorithms.

One acceptable protocol for organization H is that represented In

Figure 6. The minimum interarrival time. HT/3, is much greater than for

organization P. This is due to the relationship between transition f* and

ON*, where the information coming out of f* has to be processed by all

DMa's transitions before transition B* can be fired and the last token

leaves the place z

1

. Application of the syHstric argument of the

proposition's necessary conditions determined the mean interarrival time

as llt/3. The organization's response time is calculated quite simply in

this ess by adding all processing times along the path followed by the

original input and is ST. For more coaplez organizations, the System Array

approach la preferable for computing time delays (Tabak and Levls. 1984;

Jin. 1983).

3.3 Construction of Protocols for Decentralized Caae

It waa pointed out in section 2.2 that the only salient differences

between a centralized and a decentralized structure as defined here pertain

to transition D's processing time and the establishment of satisfactory

updating. In this section, transition D is assumed to require a total time

of T/3. which is half what was needed in the centralized configuration.

Again, this number depends greatly on the nature of the organization'a

decision support system.

Acceptable protocols for organizations P and H with decentralised

databases are given in Figures 7 and 8. respectively. The minlmun interarrival time IT and the response time RT for each organization are T and

13

ti&mMim
12T/3 for the parallel one and 10r/3 and 7T for the hlerarohlcal one.

The reduction in the XT and IT. when oonpared to the centralized

case», is due entirely to the shorter response tine of the database.

Ö

2T/3

ÖDBSA1

C« .0»

msi•SA

DBRS*

C .0'

nä&tä*1**

hO

LUo^

DM* u* M*

DBRS2

f<5

CrO-ä

T/3 ,T/S d|A

DBSA3.

C» |0S

Y

o

2T/3

W>^.

DBRS3

Figure 7. Protocol of Organization P using Decentralized Databases

16

buiUMBUa*AtfAI(AAaAAA/<AtoWAnAaAUV^^ S \. vi/<VLU WWW« WW)flU>J.>^->Jt»it wVU-kVVL-Vwv. LVIVJ
Figur« 8. Protocol of Organization H using Dacentralizad Databases

3.4 Bsmarks

Each protocol in the previous sections has been derived under some

very specific conditions, in order to nice different organizations and

different database structures comparable along the same criteria. These

results are contingent upon using similar transition processing times for

both organizational structures.

17

^i^M^i/OMMÄÖÖ^^^
The mlnlJBua allowabl« laput lnt«rarrival tine la auota greater for a

hlerarohloal organization than for a parallel one. This followa from the

ore coaplex aequenoes of tasks that bare to be performed In a hlerarohloal

organization before a new Input can be handled. The total response time Is

also greater for organization H than for organization ?, and the difference

Is due again to the Increased complexity.

The second observation is that, whatever the organization, a

decentralized database structure leada to Improved performance with respect

to time. In organization P, the decentralized structure leads to an 11%

Improvement in the response time over the corresponding centralized one.

while in organization H its leads to Improvements in both IT and HT of 9%

and 13% respectively. These results are due to the basic premise that

decentralized databases takes less time to perform the data query process

than centralized ones do. (The numerical results of the above two

paragraphs are summarized in Table 1).

TABLE 1. TIME CHARACTERISTICS OF ORGANIZATIONS P AND H

Centralized DB Decentralized DB

IT(P)

IT(H)

X

llT/3

X

10T/3

RT(P)

RT(H)

19T/3

8T

17T/3

7T

IT - Minimum Allowable Interarrlval Timet RT - Response Time

18

IflHHHAAAUHilMtoW:'^-MMMM^tiMMMKbt^^
4. AM ILLÖSTHATIVE EXAMPLE

4.1 DMcrlption of thg Orgmnizatlons tegd

In this Motion, tactical organizations, one parallel «nd one

hierarchical, are used to address the issues that arise in the qualitative

evaluation of organizations, the problens raised by a lack of coordination

between several individual databases, and the trade-off between performance

and tineliness. (The ezaaple is developed in its entirety in BeJJani,

1983).

The first organization Is the parallel one (Organization P) in Figure

S. It consists of three naval battle groups defending a maritime front.

The first group, DM1, holds one extremity of the front, DM* holds the

center, and DM* the other end. The inputs received by the organization are

signals emitted by unidentified platforms (submarines, surface ships,

planes). The different deoisionmakers' tasks are to attempt to identify

the source of these signals (enemy or friends) in the SA stage, and to

select the appropriate response (fire, request identification, or take all

measures required to face an attack) in the RS stage.

The SA database provides information, obtained from intelligence

sources, that describes the codes the enemy could use when emitting the

kind of signals received by organization P. This Information will be

compared to the actual input to determine the letter's identity. The RS

database, DBRS, informs the deoisionmakers about the level of alert present

in their area at each iteration.

The second organization is the hierarchical one (Organization H) shown

in Figure 6. The context is the same as for organization P, but here only

DM* and DM* actually receive any external signals or select an active

response. DM* is a coordinator who. based upon the situation assessments

received from DM1and DM*, gives instructions about what RS algorithm

should be selected by either of them. The organization's overall mission

is the one defined for organization P.

19

«MMMÄSa^^
4.2 BMttita

A prlaary f^atur« of the «xaapl« Is Ita nuatrloal slapllclty: all the

varlablas of the system are determined using binary logic based on the

comparison of quantities} there are no actual computations. Detailed

definition of the rarlables and the algorithms for the ease of a single

deolslonaaker has already been presented (Boettoher, 1981). The baslo step

In the computation of the performance-workload pair (J.G) Is determining

the pure strategies present In the organization (Levis and Boettoher,

1983). Zn the oases at hand, each IM has two pure strategies, each

obtained by the exclusive use of one algorithm (no deolslonsaker here has.

In any stage, more than two algorithms from which to choose). Activity

rates are a better measure of the deolslonaakers' workload than absolute

activity, because of the time constraints present In real-world situations.

The following equation applies here:

G - -2- 1 - 1,2.3 (8)

for either organization. The performance measure J is the expected value

of the cost the organization Incurs when it does not produce the correct

response for a given input. The workloads Q

1

determined by each pure

strategy and the corresponding performance level J are plotted in the

(J, G

1

, G

a

. Q

1) space. Then, the performance-workload (P-W) locus for each

DM Is constructed where all possible mixed strategies are considered as

linear combinations of the pure ones. The graphs tuus obtained are the

projections of the overall (P-M) locus of the organization on each of three

planes: (GSJ). 0

s,J), (G,,J). Because the Input is perfectly symmetric,

as well as DM1's and DM*'s roles in each organization, only the projections

for OH* and DM* are shown.

The use of activity rates in this Instance has the effect of

Illustrating very clearly the tradeoff between timeliness and workload

(Figs. 9 and 10). The performance of organization P is better than that of

B; the performance index for P takes values between 0 and 0.9 for P but

20

aBBifi^^^^
btttwMn 1.2 and 4.S for H. However, the vorkload of the oembers of P Is

uch higher than that of H. naaely. It varies between t.l bits/sec and 11.6

for P, while It la only 1.3 and 2.7 for H. Measuring workload In terms of

aotlTlty rates gives organization H a slgnlfloant advantage as far as

keeping the deolslonoakers' workload below a given axlmun (the bounded

rationality oonstralnt) Is oonoemed. However, another tradeoff appears

here that Involves the notion of tlaellness. In effect, slnoe In this

example workload Is a decreasing function of the aean Interarrlval time,

Eq. (8), low workload levels are obtained by allowing a high IT, which

penalizes the organization In terms of Its timeliness. Thus, workload Is

reduced In H. but timeliness Is sacrificed.

Another consideration of Interest is the effect of poor updating

coordination on the organization*a performance when decentralized databases

are used (e.g., Figures 7 and I). The Impact of two different updating

sequences on performance Is reflected on the (P-W) loci. In the first

scheme. DM*'s and DM*'s RS databases are assumed to be updated, at T * 0,

In coordination with the Input arrival. DM1'a DBRS, however. Is updated

at x ••> T, with a delay of x over the Input to which the data correspond.

Mew performance levels for each pure organization strategy were derived

and a performance-workload locus was drawn (see Fig. 11(a)). The main

effoots are the upward movement of the original locus, and a degradation In

performance: the range of J Is from 0.3S to 1.0 as opposed to 0 to 0.9 for

the perfectly coordinated (or the centralized) database case; this

represents a drop of 29% In the average performance of the organization.

A second scheme exhibits a less coordinated updating sequence: DBRS*

Is updated at t + 0, DBBSXat T + v, and DBRS* at v •»> 2T. DM1and DM*

both now have a greater propensity to make the wrong decision, and the

resulting (P-W) locus Is presented In Fig. 11(b). The best performance

(lowest J) Is now O.S, which Is very dose to what the worst performance

was In the coordinated case, and the worst performance level la 1.2. The

range of possible performance levels has shrunk further, and the drop In

average performance with respect to the original case Is 68%.

21

im*LmiU*VM.r^*.im*m*».^.m.^^^.~, 1||.| -,1 p, ^ ,-M^, .n „ „ njm^ij^j !

iiien<iikM.rjr>r^
Jf

4.9

4|-

3.9

3

2.5

2

t.5

lh

as

DM'

J I I L J I L

0 4 4.9 9 9.9 6 6.9 7 7.5 8 8.5 9 9.9 10 10.9 11 11.9 xi

Jt

4.5

4

3.5

3

2.5

2|-

4 4.9 9 9.9 6 8.9 7 7.9 8 8.5 9 9.5 10 10.5 it 11.5 »

Plgur« 9. (P-H) Loci for P Using Aotivlty Ha tos

22

V M JUdsfJSHIHAAMAJMm KMBlflLWMWkk > i/v uv \JU vii uuvn> L^ \juvarukt a^i AA uiiu( « ^^ ^ ^■■ ^ BUSMK'VJIv «vmii
J1

I

*-9 -

•^^

4 - N

3.5 -

kV

3 - DM1

2.5 -

2 -

1.5 - L^

1

1 -

i—•

as -

i i

, ,

• i i

0" 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 5«

Jt

4.5

4

3.5

3h

2.5

2

1.5

I -

0.5 [•

o"

DM"

—' 1 1 1 1 1 1 I ,

0.5 I 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 in

Plsur« 10. (P-V) Loci for H using Activity Bat«s

23

mmmmmmmmmmmmmmmimmmmmmmmammmmmmt*i*:**mL*jM&jto&<&tt^^
J4

4.5

4

3.5

3

2.5

2

1.5

as

' « « » I I I L J L. J I L

0*4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 II 11.5 ni

J

4.5

3.5

3

2.5

2

1.5

1 -

0.3

P- J ' « ' ' J I ' '

0 4 4.5 5 5.5 6 6.5 7 7.5 8 85 9 9.5 10 10.5 II 11.5-,

Figur« 11. (P-V) Loci for DM1in P with uncoordinated DaUbases

m^K—^mi^a—^**M
L«t tbe transition prooMalng tin« b« «qunl to t oooonds. Then IT(P)

will b« t sooonda an vail, and ITCH) llx/3 aaoonda (or 10t/3 aao.(

depending on the database oonflguratlon). In any event. IT(H) la auch

greater than ZT(P) and nay handicap organization B If It has to respond to

threats arriving at a high rate. As an example, consider a wave of enemy

planes attacking the battlegroup: Zf no defense can be Initiated without

processing every Input through the SA stage, then the anti-aircraft

batteries cannot ahoot at a rate higher than one aissile every 3.6x sec.

Zf a nav threat arrives once every x aaoonda, then P is an adequate

structure, while H is far froa being one. An additional disadvantage of

organization B appears when response times are taken into account: the

battlegroup will need 8x aaoonda to fire on a threat after it la detected}

this might be too long if tbe threat is very close to the battlegroup when

its presence is detected.

When the platforms that the organization has to deal with are alower

units, like submarines or surface ships, organization B's timeliness

disadvantage is less critical, because of the longer time available for

constructing an adequate response and because of the smaller threat arrival

rate. In facw., the latter can be so small as to make any difference

between ZT(P) and ZT(B) seem irrelevant. Since the organizations designed

in this example have to deal with both alow and fast threats, one has to

consider the relative probability of being attacked by fast or slow

threats, and weigh it by the expected costs in each alternative during the

evaluation of the two organizational structures,

S. CONCLUSION

In this paper, the use of database networks was Introduced into the

organization, in two alternative configurations: centralized, and

decentralized. Information theoretic aspects of data storage devices were

analyzed. Time-related consideration were preaented and used to create new

criteria for the evaluation of the organization. The example illustrated

the major theoretical results.

25

**>***ÜMMMM^^ vCVttJttttl
$. REFEREMCES

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ft

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27

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