%

x ;• W^ J

NBS TECHNICAL NOTE 782

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

pplication of Systems

Analysis to the Operation

of a Fire Department

1*1 Vi 'j»Jl'iBm«BBWaHgMBH
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology,

the Institute for Computer Sciences and Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

States of a complete and consistent system of physical measurement; coordinates that system

with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of a Center for Radiation Research, an Office of Measurement Services and the following divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Nuclear

Sciences 2 — Applied Radiation ° — Quantum Electronics 3 — Electromagnetics 3 — Time

and Frequency " — Laboratory Astrophysics " — Cryogenics ". THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized

materials needed by industry, commerce, educational institutions, and Government; provides

advisory and research services to other Government agencies; and develops, produces, and

distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials and the following divisions: Analytical Chemistry — Polymers — Metallurgy — Inorganic Materials — Reactor

Radiation — Physical Chemistry.

THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services to promote

the use of available technology and to facilitate technological innovation in industry and Government; cooperates with public and private organizations leading to the development of

technological standards (including mandatory safety standards), codes and methods of test; and provides technical advice and services to Government agencies upon request. The Institute consists of a Center for Building Technology and the following divisions and offices: Engineering and Product Standards — Weights and Measures — Invention and Innovation — Product Evaluation Technology — Electronic Technology — Technical Analysis — Measurement Engineering — Structures, Materials, and Life Safety * — Building

Environment 4 — Technical Evaluation and Application * — Fire Technology.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improving cost effec- tiveness in the conduct of their programs through the selection, acquisition, and effective

utilization of automatic data processing equipment; and serves as the principal focus within

the executive branch for the development of Federal standards for automatic data processing

equipment, techniques, and computer languages. The Institute consists of the following

divisions: Computer Services — Systems and Software — Computer Systems Engineering — Information Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and

accessibility of scientific information generated within NBS and other agencies of the Federal Government; promotes the development of the National Standard Reference Data System and

a system of information analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services to ensure that the NBS staff has optimum

accessibility to the scientific information of the world. The Office consists of the following

organizational units: Office of Standard Reference Data — Office of Information Activities — Office of Technical

Publications — Library — Office of International Relations.

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

2 Part of the Center for Radiation Research.

3 Located at Boulder, Colorado 80302.

* Part of the Center for Building Technology.
4 1974

\cc.

I

Application of Systems

Analysis to the Operation

of a Fire Department

Ernst K. Nilsson, Joseph A. Swartz, and

Marilyn Westfall

Technical Analysis Division

Institute for Applied Technology

{J, 5, National Bureau of Standards

rrr Washington, D.C. 20234

TeaMrCjfl-P ncrte- rie>, 752.

* r 3ii&7

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued June 1974

aiHHHHnaniiBi
Library of Congress Catalog Number: 74-600079

National Bureau of Standards Technical Note 782

Nat. Bur. Stand. (U.S.), Tech. Note 782, 52 pages (June 1974) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1974

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. 03.46:782). Price 90 cents
TABLE OF CONTENTS

Page

1.0 INTRODUCTION 1

1.1 Purpose of Paper 1

1 .

2

Scope of Paper 2

1.3 Project Initiation 2 1.4 Operations Research 2

2.0 ALEXANDRIA, VIRGINIA 3

2.1 City Background 3

2.2 Organization of the Fire Department 5

2.3 Emergencies 6

2.4 Other Activities 8

3.0 DATA COLLECTION AND TABULATION 9

3.1 Calls for Service by Time of Day 9

3.2 Calls for Service by Type 14

3.3 Calls for Service by Service Time 17

3.4 Calls for Service by Location 17

4.0 APPLICATION OF QUEUEING THEORY 22

4.1 Availability Analysis 22

4.2 Assumptions 23

4.3 Application 25

5.0 APPLICATION OF LOCATION MODELS 29

5.1 Assumptions 30

5.2 Maranzana 31

5.3 REDIST 33

6.0 SIMULATION 36

6.1 Simulation Model 36

6.2 Assumptions 36

6.3 Simulation Model Input and Output 37

6.4 Evaluation of Location Alternatives • ^0

7.0 CONCLUSION 45

in
Table l.A.

Table l.B.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

Table 8.

Table 9.

Table 10.

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 Tables

Frequency of Calls for Service by Eight Hour Periods

for 123 Days of Calls: First Breakdown ••••••••: •;,• Frequency of Calls for Service by Eight Hour Periods

for 123 Days of Calls: Second Breakdown . . ... ...... Average Number of Calls for Service per Day by Type

and Time Period : • • • • • • • • • • • • • • • • •

* '

'

* *

* Number of Days Having a Specified Number of Calls

-Pq-p Service

Average Service Time (in minutes) by Type of Alarm

Frequency Distribution of Service Times for Alx

Calls Tin five minute intervals) • • • • Number of Calls and Time Out of Station by Company ...

.

Probability of n Number of Calls/Hour for Different

TlSreUca^

13

13

15

15

18

18

19

26

28

39

41

7

10

11

Period for Alexandria

Availability Distribution Using Chaiken and

Simulation Models ; Statistics for Different Alternatives

List of Figures

Alexandria, Virginia: Distribution of Population

by Census Tract, 1970 Census : mm "':

Locations of Alexandria's Engine Companies (E)

,

Truck Companies (T) , and Rescue Squads (R) -

City of Alexandria, Virginia Fire Department

Company Report Form

TAD Fire Study Data Form • • •

;

• •

• Distribution of Calls by Hour of Day During a 123 ^

Day Period ' * * * *

° 16

Distribution of Calls by Type of Call ••••••• • • —• ' '

' ; 2Q

Calls for Service by Location 0V

^,

aD

^3

p

^ ^

ri°d

. '.

'. 21

False Alarms by Location over a 123 Day Period ^

Service Time Distributions 32

Sample of Cells , and Coordinate System ^

Sample Location Output: Maranzana

35

Sample Location Output: REDIST ••••••;• ••''''''' v^aine

Distribution of Response Times for Last Arriving Engine

when One Engine Company is. Dispatched ;••;;:;:;• '^vike

Distribution of Response Times for Last Arriving bngme

when Two Engine Companies are Dispatched •••• — • —

Distribution of Response Times for Last Arriving bngme

when Three Engine Companies are Dispatched

42

43

IV

44
AN APPLICATION OF

SYSTEMS ANALYSIS TO THE

OPERATION OF A FIRE DEPARTMENT

Ernst K. Nilsson*

Joseph A. Swartz, Jr.**

Marilyn Westfall

Rising labor costs and increasing competition for tax

dollars to provide urban services demand that a more precise

methodology be used in the management of fire departments

.

A pilot program was conducted with the cooperation of the

Alexandria, Virginia Fire Department to evaluate the applicability and usefulness of selected Operations Research tools.

These tools, in the form of computer models, were modified

and adapted to assure that they could be implemented to

provide information which would facilitate fire department

management. In this effort queue ing, facility location,

and simulation models were applied to sample data extracted

from the historical records of the Alexandria Fire

Department. It was established that such models do provide

valuable information which may assist managerial decisions.

This paper describes the city of Alexandria and its fire

department, the O.R. models, output from their application,

and evaluations of the output.

Keywords: Alexandria; fire department; location; operations

research; resource allocation; simulation; systems analysis.

1 . INTRODUCTION

1.1 Purpose of Paper

This paper documents the application of Operations Research management

tools to decision problems arising in the planning and provision of fire

department services. The purpose of the paper is to demonstrate the

utility of such an approach to city managers, planners, fire service

officials, and other personnel unaccustomed to O.R. methodology.

Therefore, an attempt has been made to exclude highly technical

expositions. Instead, references are given to individual reports

published by the Technical Analysis Division (TAD) of the National Bureau

of Standards (NBS) which detail the mathematical procedures employed in

the various models.

* Present address: Osterlanggatan 20, 111 31 Stockholm, Sweden.

**Present address: National Fire Prevention Association, 60 Batterymarch

Street, Boston, Massachusetts 02110.

1
1 . 2 Scope of Paper

This paper is based on a study done with the assistance of the

Alexandria, Virginia Fire Department. Sections are included on each of

the three major methodologies that were developed. The paper should be

regarded as a practical demonstration that quantitative analysis can be

useful to city and fire department decision makers.

1.3 Project Initiation

The Technical Analysis Division of the National Bureau of Standards was funded in June 1970 by the Office of Fire Research and Safety to

demonstrate the applicability of Systems Analysis and Operations Research

techniques to fire service problems. TAD contacted the Alexandria

Fire Department for permission to use their actual engine and truck

company reporting forms for the period of May through August, 1970.

The fire department was also requested to identify local problems for

solution. The major question posed by the Alexandria Fire Department

concerned the probable effects of proposed changes in their pattern of

fire station locations.

1.4 Operations Research

Operations Research (O.R.) developed in response to the increasing

need for efficient and scientific methods to study problems involving

the interaction among various operational units within more complex^

organizations. The field employs scientific methods, techniques, and

structures to analyze problems involving the operations of a system of

activities so as to delineate for management alternative choices of

action or decision. O.R. has evolved a methodology drawn from the

appropriate aspects of mathematics, social science, and the physical

sciences to provide problem solving techniques for problems of an operational nature. The general procedure is to:

1. Study the objectives of a system and determine the essential

factors - the cause-effect relationships - involved in its

operations

,

2. Determine and implement a way to measure the essential factors

and collect the pertinent data

,

3. Construct a model to represent the system under study,

4. Derive various practical solutions from the model,

5. Test the methodology and the solutions derived from its use,

6. Use the solutions to suggest courses of action which will

further the goals of the system [1]

.

1

l Figures in brackets indicate the literature references at the end of

this paper . 2
This study applies the above methodology, using several different

types of mathematical models. The specific applications will be

discussed in detail in later sections.

Section 2 describes the city of Alexandria and the particulars of

its fire department. Section 3 discusses the data which was collected

and how it was tabulated. Sections 4, 5, and 6 apply different methods

of analysis to the data to answer specific questions. Section 7 is a brief summary of the paper.

2.0 ALEXANDRIA, VIRGINIA

2.1 City Background

The city of Alexandria, Virginia covers an area of 15.3 square miles,

and listed a population of 110,938 persons in the 1970 census. The

population increased by 19,915 persons from the 1960 figure, but the

increase was appreciably smaller than that of the preceding years

Census Year Population Increase from Previous Census

1950 61,787 29,264

1960 91,023 29,236

1970 110,938 19,915

The distribution of the population by census tract is presented in

Figure l. 2

Alexandria is the site of the largest railway switching stations on the Eastern Seaboard; Potomac Yards covers 520 acres. The Port of

Alexandria has a busy traffic in newsprint and stock for the many import

and specialty shops in the area. Because the city is so heavily

residential, there is little space for large and heavy industry. However,

there are many smaller manufacturers producing such items as pre -cast

concrete, chemicals, fertilizers, mattresses, flags, and foundry castings.

Over 30 percent of the total work force is employed by the federal

government in nearby Washington, D. C. , and many more work for firms

holding government contracts. The cash income level of the inhabitants

ranges as follows

2 In future planning studies, projections of population growth will be

needed in order to base station locations on anticipated demands for

service.

3

Family Income Percentage of Population

$0-2,999 9.2%

$3,000-4,999 10.1%

$5,000-7,999 23.6%

$8,000-9,999 15.8%

$10,000-over 41.3%

Alexandria has a total of 44,426 housing units, approximately 1,950

of which are vacant. Almost half of the occupied units consist of 29,750

garden apartments, which have become the predominant type of housing in

the last ten years. In addition to 16,000 family homes, there are 8,884

high rise units, 90 percent of which were constructed in the last decade.

Considerable redevelopment has been completed in the older eastern portion

of the city. In the western sector, new housing projects have been

initiated. The Alexandria Redevelopment and Housing Authority administrates

1,034 public housing units which house a total of 4,075 inhabitants.

Alexandrians are acutely aware of the historical significance of

their city, one of the earliest towns to be incorporated after the

American Revolution. Careful preservation and restoration of historical

sites receives great emphasis in city planning.

2.2 Organization of the Fire Department

The Alexandria Fire Department is funded by local city taxes.

During the 1970 fiscal year, the city's fire protection services cost

the average family of four approximately 25 cents per day in taxes.

Expenditures by the fire services for the same time period totaled

$4,984,600. This amount was budgeted for:

Category Amount in Dollars

personnel services 2,294,990

non-personnel services 109,885

capital outlay 88,520

administration 104,595

firefighting 1,786,345

fire prevention 143,830 rescue 169,795

maintenance 113,390

communications 129,635

training 43,615

Alexandria's fire department engages 184 employees, all of whom are salaried personnel. They are assigned to the following permanent duties:
Duty Number of Employees

administration J

firefighting ^6

fire prevention H

rescue squad 12

maintenance ' communications ° training 3

Each

The fire department system is comprised of seven fire stations;

. station ho^es one engine company composed of one or two pumpers with

are shown in Figure 2.

The fire department responds to emergencies and carries on various

other appropriate activities.

2 . 3 Emergencies

The fire department received a total of 2,693 alarms in 1970 which

were classified in the following manner:

Actual Fires

703

in buildings

R brush, grass, woods

"°

trash and litter

"°

miscellaneous outdoor fires

^

vehicles on streets iioy

Other Alarms

accidental 86

481 public service

553

false

fires out of city 34
r

Figure 2

Locations of Alexandria's Engine Companies (£)

,

Truck Companies (T) , and Rescue Squads (R)

ARLINGTON CO.

FAIRFAX CO

FAIRFAX

MARYLAND
The rescue squad responded to a total of 6,958 emergencies. The

general procedure is to transport all victims to Alexandria Hospital on

Duke Street, and then if necessary to transfer them to a hospital which

can treat their specialized ailment or injury.

The fire department also participates on a standby basis in riot

control

.

2.4 Other Activities

The fire department is responsible for its own cooking, housekeeping,

building maintenance, and equipment repair. In 1970, 6,000 hours of

training sessions were conducted occupying 21,500 man hours.

During 1970 the fire department conducted a total of 7,836 fire

safety inspections of the following premises:

public buildings 432

dwelling occupancies 3385

mercantiles (warehouses, offices,

stores, restaurants) 2325

manufacturing 391

miscellaneous buildings (railroads,

wharf property, oil storage, etc.) 1303 ,

\

In May of each year, Fire Service Day is held to acquaint citizens

with their fire service and its role in the community , through talks, open

houses, and tours through the fire stations.

An annual fire prevention week program promotes fire prevention courses and regular drills in public schools , the elimination or protection of

sub -standard buildings, the installation and checking of sprinkler alarm

systems and first aid equipment in industrial and mercantile buildings,

and clear marking of eacits in public buildings.

A miscellaneous assortment of community services are continually

provided, including:

replacing flagpole ropes

rescuing stranded children and animals

collecting muscular dystrophy funds

giving lectures, demonstrations, and film presentations on

fire hazards

conducting practice evacuations in hospitals, nursing homes,

and commercial establishments

handling complaints

checking foster homes.
3.0 DATA COLLECTION AND TABULATION

A total of 123 days of data was collected covering each engine and truck

company response during May, June, July, and August, 1970. The data was

taken off the company report form (see Figure 3) which is filled out by

each truck and engine company responding to an alarm. TAD personnel

transferred the data items to the computer compatible data form shown in

Figure 4.

As the data sample was limited to four months, any conclusions pertain

strictly to that limited time period. However, the data analysis is

illustrative of possible procedures.

Once the forms had been completed, the information was reviewed and

certain factors were tabulated, including the distribution of calls tor

service by:

A. Time of day

B. Type of call

C. Service times and resource utilization

D. Location.

3.1 Calls for Service by Time of Day

The calls for service (CFS) were distributed by time of day as shown

in Figure 5. A marked increase in demand during the evening hours is

visible. The variation in frequency of calls is highlighted by dividing

the day into the three time periods used in Table 1A. This breakdown

shows twice as many CFS during Period III as during Period I. Other

temporal divisions are possible, as in Table IB. The difference in demand

load is still evident.

For the 123 day period, the average number of calls per day was 7.73.

The average per period was:

Time Period Average Number of Calls for Service

0001-0800 1.47

0800-1600 2.44

1600-2400 3.82

7.73

This information suggests that if there is a temporary manpower shortage,

it might be desirable to ensure sufficient personnel for the third period

rather than to assign equal numbers of employees for each period. If

such averages were computed by company for a larger sample, preferably

a complete year, they could be used to compare work loads and adjust

personnel assignments for the individual companies. Seasonal changes in

these norms could be used to determine the establishment of leave

periods and policies

9
F-O. roRH 4 •u—4-ee

Figure 3 CITY OF ALEXANDRIA, VIRGINIA

FIRE DEPARTMENT

Company

Monthly NumberAnnual NumberDate __

Location of Alarm

Type of Alarm Time of Alarm '. Time in Service. Source of Alarm Received by __. Number of Stories in Building Construction of Building __ Occupancy of Building Location of Fire _.... Origin of Fire .. _ Owner of Building, Property or Vehicle Occupant or Tag of Vehicle Insured- Uninsured Agent _ AmountInsurar.ee Property Amount Insurance Contents Was There Damage to Property? Damage to Contents? _ Was Pump Operated? Time Operated _ Size Pump

Was Booster Used?. Time Operated

Hydrant Stream Used? Time Used _ Location and Condition of Hydrant y.~

Size and Feet of Hose Line Used: 3 inch 2*/2 inch

1 Vi inch Booster _._ Apparatus Answering Alarm _

Drivers _ Number of Men Responding Number of Men Injured Number Killed. Name and Nature of Injury

Type and Number of Extinguishers Used.

Salvage Covers Used Left at Scene Other Tools Used .

Feet of Ladders Used: Single Extension Aerial.. Damage/Loss of Equipment:

Damage to Apparatus:

Citizens Injured by Fire

Citizens Killed by Fire : Department Officer in Charge.—.

Company Officer in Charge

Tract Remarks

10 Signed,.

Title

10
Figure 4

FIRE STUDY

[TAD Form]

1. Annual No.

2. Address:

3. Type of alarm:

12 3

5 6 7

1

tt Public Service

2 = Special

3 = Malicious alarm

4 = Accidental alarm

5 = No fire

6 = Fire

7 = Mutual Aid Assignment

4. Units responding:

engine = 1 or 2 truck = 3

Time Out

c U

34

d . U

46

58

1

!111 1 u

j

1 14

23

i

!

26

, ! i 35 38

i 47 50

59

1

62

1 1 !

, Time In

i

! 15

V

i

18

i 1

i 1 27

!

1

J

30

39

1 I

J

42

51

! 1 I

54

1

i

i 63

! 1

i

66

i

Pump Op.

(min)

i_L_

19 20

3T 3T

43 44

i i i 55 56

No. of

Men

21

33

45

57

67

68 69 72 73 76 77

5 . Date

78 79 80

day month

11
Figure 5 Distribution of Calls by Hour of Day

During a 123 Day Period

Number of

Calls Occurring

Hour in Hour

1

2

3

4

5

6

7

8

9

10

11

12

50

38

30

24

13

7

8

15

22

24

29

36

80

70

60

Fraction of

Total Number

of Calls

0.052

0.040

0.031

0.025

0.014

0.007

0.008

0.016

0.023

0.025

0.030

0.038

Number of Fraction of

Calls Occurring Total Number

Hour in Hour

13

14

15

16

17

18

19

20

21

22

23

24

36

59

50

48

33

73

50

63

49

70

62

72

>!

of Calls

038

,061

052

050

034

076

052

066

051

073

0. 065

0. 075

10 12 14 16 18 20 22 24

Hour of Day

12
Frequency of Calls for Service by Eight Hour Periods

for 123 Days of Calls

Table l.A.

First Breakdown

Period Time Period Frequency of Calls Percent of Total Calls

I 0001 - 0800 185 19.3

II 0801 - 1600 304 31.6

III 1601 - 2400 472 49.1

961 100.0

Table l.B.

Second Breakdown

Period Time Period Frequency of Calls Percent of Total Calls

I 0101 - 0900 157 16.3

II 0901 - 1700 315 32.8

III 1701 -- 0100 489 50.9

961 100.0

13
Statistical tests were also conducted to examine variations in the

number of calls for service by day of the week, but no statistically

significant difference was found. This is an unusual finding since such

differences were found for data collected by NBS for other cities.

It was not appropriate to tabulate the distribution of service calls

by month of the year because of the limited sample.

3.2 Calls for Service by Type

The calls for service were divided into three types

:

1. Public Service and Special Services

Public service calls involve a non-fire and non-hazard

related service such as replacing a flagpole rope or rescuing a cat in a tree. If a hazard exists which the

fire department is specifically equipped to handle, such

as draining a water -filled basement or washing down a street after an accident, the call is designated as a special service call.

2. False Alarms

If an alarm is given with malicious intent when there is no actual fire, 3 the call is considered a false alarm.

3. Suspected Fires, Real Fires, and Accidental Alarms

A suspected fire is an alarm given with good intent

because the caller mistakenly assumed a fire from such

signs as smoke from a stove grease fire or burnt bearings

in a furnace fan. A real fire consists of smoke and

flames. An accidental alarm occurs due to such mechanicall

malfunctions as a water surge in an automatic sprinkler

system.

The average number of calls for service per day by type during the three

time periods was tabulated and is shown in Table 2.

Table 3 shows the distribution of the number of days having a given

number of calls for service of the various types. For example, there

were 24 days during the 123 day period when two Public Service calls

occurred. There were five days when there were zero calls for service.

This information is presented graphically in Figure 6.

3An alarm is considered to have been given with malicious intent when

no fire is found and the caller has left the scene.

14
Table 2

Average Number of Calls for Service per Day

by Type and Time Period

Type/Time Period 0001 - 0800 0800 - 1600 1600 - 2400 Total

Public Service

False Alarms

Suspected and

Real Fires

.49

.54

.44

1.35

.33

.76

1.76

1.04

1.02

3,60

1.91

2.22

Total 1.47 2.44 3.82 7.73

Table 3

Number of Days Having a Specified Number of Calls for Service

Number of Number of

Number of Calls Number of Days Number of Days Days Having Days Having

for Service Per Having (N) Public Having (N) (N) Real Fire (N) Total

Day (N) Service Calls False Alarms Calls Calls

6 23 23 5

1 8 34 30 1

2 24 32 23 4

3 22 17 22 4

4 31 10 10 9

5 14 2 6 10

6 7 2 6 16

7 8 2 1 17

8 2 1 19

9 9

10 1 1 9

11 1 7 12 5

13 3

14 2 15 1

16 1

17 1

15
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3.3 Calls for Service by Service Time

Service time is defined as the total time that a company devotes to an alarm. This includes travel time to the scene , time spent handling

the alarm, and return travel time.

The concept of service time is useful since knowledge of average

service time by type of call provides a quantification of the different

demands on company time. In addition, both the average number of calls

per day and the service times are needed for the analysis in Section 4.

Table 4 shows the average service time for the various types of calls;

Table 5 shows the frequency distribution of service times for all calls.

Engine and truck companies are defined here as the resources available to handle alarms. An important factor is the amount of time that

these resources spend handling alarms. Table 6 shows the number of calls

handled by each company, as well as the number of minutes each company

spent handling calls during the 123 day period. The last column in

the table was derived in the following manner. The number of minutes

from the previous column was divided by the total number of minutes in

the 123 day period (i.e., 123 days x 24 hours x 60 minutes=177,120 minuteg).

The result is the percentage of work time spent actually handling alarms.

These percentages are averages for the total 123 days.

3.4 Calls for Service by Location

Figure 7 shows the geographic distribution of calls for service

in Alexandria, Virginia on a grid of 1500 foot square cells. It is

evident that the calls over the 123 day period tend to cluster. This

clustering has possible implications for fire station location, assignment,

and unit relocation policies. The distribution by location of false

alarms throughout the city is shown in Figure 8. The geographic

distribution of calls for service could be further specified by time

period and/or by type of call. Changes in patterns of alarms could then

be correlated to demographic or seasonal changes to provide information

useful for suggesting or evaluating such proposed new procedures as tactics

to reduce false alarms.

There are indications that the incidence of fire alarms is associated

with the socio-economic characteristics of different areas of the city.

For example, the New York City Rand Institute [2] has found a high

correlation between fire department and police department calls for service,

with respect both to time of occurrence and to location.

17
Table 4

Public Service

Special Services

False Alarms

Accidental Alarms*

Suspected Fires (smoke.

etc.)

Real Fires

le (in minutes) by Type of Alarm

Average Service Time Number of Calls

in Minutes in 123 Days

22.12 249

24.84 191

9.59 241

80.16 19

18.72 137

33.16

124

Total 961

Minutes

- 5

5

- 10

10 - 15

15 - 20

20 - 25

25 - 30

30 - 35

35 - 40

40 - 45

45 - 50

50 - 55

55 - 60

60 - 65

65 - 70

70 - 75

75 - 80

> 80

Table 5

Frequency Distribution of Service Times

For All Calls (in five minute intervals)

Number of Calls Percent of Calls

23 2 198 21

216 23

153 16

96 10

56 6

47 5

48 -4 20 2 13 1

18 2 7 1

7 1

16 2 7 1

5 1

22 2 952** 100%

Mean = 22.10 minutes

Standard Deviation = 17.58

The long average service times for accidental alarms occur because the

fire department must wait for the representative of the alarm company,

determine that there is no fire, and find the cause of the automatic

system malfunction.

**Nine cases were not included because of insufficient data.

18
Table 6

Number of Calls and Time Out of Station by Company

Minutes Spent

Engine Co. Number of Calls Handling Alarms Resource Utilization

1 147 3806 2.2%

2 137 4635 2.6

3 123 3617 2.0

4 228 5013 2.8

5 221 8192 4.6

6 133 3042 1.72

7 130 3827

average

2.1?

2.6%

Minutes Spent

Truck Co. Number of Calls Handling Alarms Resource Utilization

1 143 3622 2.0%

2 82 2319 1.3

3 74 2184 1.2

4 76 2085 1.8

average 1.6%

19
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21
Data displays, like those shown in this section, are useful for

developing an intuitive understanding of the demand for services and the

resource utilization in a fire department, and for determining the origin

locations of alarms of different types.

Where and when demands for service occur evidently has implications

for the number of resources needed and their proper locations. However,

further analysis is necessary in order to answer these two questions.

Section 4.0 utilizes Queueing theory to analyze the temporal aspects

of demands for service. Section 5.0 implements concepts of Location

theory to generate and assess various fire station location patterns. The

alternatives provided by Sections 4.0 and 5.0 are then evaluated in

Section 6.0, using a simulation model capable of combining both temporal

and spatial aspects.

4.0 APPLICATION OF QUEUEING THEORY

Analysis of a resource allocation problem often involves determining

the necessary number of resources required to handle demands for a specific

service when the demands arise randomly. Such demands might originate

from supermarket customers at check-out counters, phone calls at a switchboard, or citizens requiring police or fire service. The common

element is that there are identifiable demands for service which occur

randomly.

Queueing theory - so called because it concerns the properties of

waiting-lines or "queues" - is a mathematical tool which is useful in the

consideration of such questions. It provides means for characterizing the

rate at which demands arise, the rate at which service is provided, and

the effect of both rates on the ability of the system to respond.

For instance, customers in a supermarket having only one check-out

counter may have to wait in line so long that they become impatient and

leave the store. Management can furnish additional counters to relieve

the delay in service, but there is a fixed cost associated with each

manned counter in terms of construction and salaries. Some balance must

be established between increased cost and customer inconvenience.

4.1 Availability Analysis

The adaptation of Queueing theory to the fire services is primarily

concerned with insuring that "enough" resources will be available when

needed. "Enough" is a policy variable that the local jurisdiction must

determine in accord with its economic and political situation.

22
Queueing theory provides estimates of resource utilization, the

probability of an alarm having to wait before being served, and the

probable length of the wait. This type of analysis, applied to fire

services, will be referred to as Availability analysis. Fire alarms

represent demands for service, and the number of engine and truck

companies constitute the resources.

Availability analysis provides a fire chief with such specific

information as: "the incidence of a citizen calling for aid when no equipment is available to provide service will (on the average) occur

once in four years with seven companies, and one in forty years with

eight companies." He may then calculate the costs of providing the

two different levels of protection (seven or eight companies) , and

the average and maximum times callers may expect to wait for an emergency vehicle in each instance. Such data, together with a "per company" cost figure, would inform the citizens as to how much

they would have to pay for a specific capability of this vital

urban service.

4.2 Assumptions

Availability analysis makes certain assumptions about the behavior

of demands for service and the time it takes to service them [3] . As

applied here, it assumes that the times at which demands arise can be

modeled mathematically using a "Poisson distribution". This implies

that the individual calls for service occur randomly, that the times at

which they arise are independent of the pattern of arrivals of

previous calls, that there is no periodicity in the pattern of calls,

and that the probability of two or more calls arriving within a very

short time interval is essentially zero.

This assumption of Poisson distribution of calls for service was tested for the 123 days of historical data collected in Alexandria.

Although the rate of arrival of the calls , was assumed to be constant

during average periods of the day, this rate changes, from period to

period, with peaks and valleys in the data. The hypothesis was that

the distribution of actual arrival times of calls for service to the

Alexandria Fire Department during each period was the same as the

mathematically predicted distribution except for reasonably likely

chance variations. A standard statistical (Chi-Square) test was employed to test the acceptability of this hypothesis, and it was ascertained that the hypothesis could not be rejected at the \% level of

significance. Therefore, the assumption of Poisson arrival rates was

accepted as consistent with the data.

At first the additional hypothesis was made that service times follow

a "negative exponential" distribution. This implies that each service

time has a constant probability of termination in the next small increment

of time, regardless of how long service has already been in progress. One

characteristic of this distribution is that the mean is equal to the

standard deviation. For the Alexandria data, the service time distribution

had a mean of 22.10 minutes and a standard deviation of 17.58 minutes.

A Chi-Square test was again used, this time to test the hypothesis that

23
the empirical service time distribution was negative exponential. This

hypothesis had to be rejected at the II level of significance. The next

simplest "standard" probability laws for service times (Erlang distributions

for k = 2, and 10) were also tried, but had to be rejected at the 1%

level of significance.

Figure 10 shows the negative exponential, Erlang and constant service

time distributions. The vertical axis is the probability, P(t) , of a service time being greater than t. The horizontal axis is time (t)

measured in average service units (T)

.

Figure 9

Service Time Distributions

a = Negative exponential distribution (k

b = Erlang distribution for k = 2 c = Erlang distribution for k - 10

d = Constant service time distribution

= 1)

The dotted line represents the actual time distribution from the Alexandria

data. It is evident that there are fewer short and very long service

times in comparison to the negative exponential distribution.

This means that the actual service time distribution is more regular

than the negative exponential distribution, though, of course, less so than

the constant (i.e., "completely regular") service time distribution.

Therefore, if the negative exponential distribution were used to estimate

the behavior of the system, it would overestimate the expected queue

length, the probability of a wait in queue, etc. It is useful to have an analytical method to obtain approximations to measures of the performance

of a system, and the negative exponential distribution was used here to

estimate upper bounds for such measures. For example, the actual average

queue lengths and the probability of a wait before a call can be handled

will always be less than those predicted by the model.

24
4.3 Application

Availability analysis was applied to the sample data collected in

Alexandria.

The questions to be answered were:

1. How many companies are needed?

2. What percentage of their total time is spent answering

alarms?

3. What is the chance of a given number of alarms occurring

per hour?

4. What is the chance that there will be no equipment

available for assignment when an alarm occurs?

5. What is the probability of having to service a given

number of alarms simultaneously?

The Poisson distribution was applied, using the historical arrival rates

(calls per hour) of calls for service. Since demands for service change

as a function of the tine of day, the days were divided into three time

periods (0000-0800, 0800-1600, 1600-2400), to account for gross differences

in the hourly level of demands for service. The average number of calls

in each time period was then divided by the number of hours (8) in that

time period to find the average arrival rate per hour. A peak load

estimate was arrived at by determining how many calls during the 123 day

period occurred during each hour of the day, then dividing the highest of

these numbers of calls by the 123 total days. This resulted in a peak

hour average of 1.08 calls per hour.

Table 7 shows the chance of receiving a given number of calls in

any given hour, assuming the arrival rates thus determined. It is read

as follows : If the average number of calls coming into the system is

3.82 during the 1600 to 2400 (4:00 p.m. - midnight) time period, there

is a 621 chance that no alarms will be received during any specific hour

in that time period.

The probability that a given number of companies will be unavailable

for a call for service because they are handling prior calls was determined

using a model developed by Jan Chaiken at the New York City Rand Institute. [4]

Data from the third time period (1600 - 2400) was used to illustrate the

effects of a higher level of demand.

First, the arrival rate of calls to which 1, 2, 3,...,n, engine

companies were dispatched was tabulated. Next, the average time that

there were X (X = 1, 2, ..., n) units at the scene was calculated. For

example, when three companies were dispatched it was necessary to determine

how long, on the average, there were three, two and one engine companies

on the scene.

25
Table 7

Probability of n Number of Calls/Hour

for Different Time Periods

Time

Period

Arrival

Rate

Calls/ Hr.

n

1 2 3 4

daily rate 7.73/24 .7246 .2334 .0376 .0040 .0003

1600-2400 3.82/8 .6203 .2962 .0707 .0113 .0013

0800-160CT 2.44/8 .7371 .2248 .0343 .0035 .0003

0000-1800 1.47/8 .8321 .1529 .0140 .0009 .0000

peak hour

0001

load 1.08/1 .3396 .3668 .1981 .0713 .0193 .0042 .0007 .0001

26
The Chaiken model assumes negative exponential service times. In

addition, it assumes that, for a given dispatch, the durations of

successive stages of service are independent and that the number of units

engaged decreases from stage to stage. A stage of service is defined as that

period during which a particular number of units are engaged at the scene.

This model is very flexible and can be used to analyze changes in

arrival rates, dispatch policies, and service times for different types

of calls for service.

Table 8 shows the availability of engine companies in Alexandria

during the 1600-2400 time period. The probability that six companies

will be occupied at the same time during the eight hour period is 0.001, or once in 1,000 eight hour periods. In this instance, the probability

that more than six companies will be occupied at the same time during

an eight hour period is also 0.001, or once in 1,000 eight hour

periods

Another measure of interest is the probability that there will be

some delay before an adequate response unit can be assigned to a call

for service. Queueing analysis provides this measure in terms of the

number of "servers" available. A fire department dispatches different

numbers of engine companies to different types of calls . The dispatch

policy varies, for example, according to whether the department has

been asked to pump out a basement or to respond to a fire alarm. During

the 123 day period the maximum number of engines dispatched for any

single call was three. Taking a conservative position, it was assumed

that three engine companies were dispatched to all calls for service.

In queueing theory parlance, this is equivalent to making the three

engine company dispatch equal to a server. Then:

(1) The probability that sufficient engine companies are not

available when an alarm occurs is (using third shift data)

For 6 Companies (2 servers) For 9 Companies (5 servers)

0.0107 0.0005

In other words, if the fire department had six engine companies

and always responded with three companies to each alarm, some delay in response would be expected, given the arrival and

service rates for the 1600-2400 time period, roughly one time

out of 100 alarms; i.e., 100 times out of 10,000 alarms. If

there were nine engine companies , some delay would be

experienced only five times out of 10,000 alarms.

27
Table 8

Theoretical Model of Availability During

the 1600-2400 Period for Alexandria

N

Probability of

Companies Busy

(N)

Probability of the Number of

Companies Busy Being Greater

than (N)

.809 .191

1 .107 .084

2 .031 .053

3 .043 .010

4 .006 .004

5 .002 .002

6 .001 .001

7 .0002 .0008

8 .0001 .0007

28
(2) The probability that there will be a specific delay before

enough companies become available is:

Probability of Waiting Time Greater Than (T) Minutes; Third

Shift Data

Time (T) Min . 6 Co. 9 Co .

10.0 .0064 .0003

9.0 .0068 .0003

8.0 .0071 .0003

7.0 .0075 .0004

6.0 .0078 .0004

5.0 .0082 .0004

4.0 .0086 .0004

3.0 .0091 .0004

2.0 .0095 .0005

1.0 .0100 .0005

.5 .0102 .0005

.25 .0104 .0005

In each time interval, the chance that response to a call for

service will be delayed when there are six engine companies is

more than ten times as great as the chance when there are nine

engine companies.

(3) The fraction of time that the companies will be servicing calls

is:

6 Co . 9 Co .

2.5% 1.71

The actual utilization factor of 2.6% for the Alexandria Fire

Department's present seven companies agrees well with the

numbers predicted by the model.

5.0 APPLICATION OF LOCATION MODELS

If unlimited funds were available to supply resources, the Fire

Department could theoretically maintain individual stations to protect

each city block. However, since public service facilities are constrained

by budget provisions, it is necessary to assign the available resources to

the best strategic locations to ensure maximum effectiveness. Location

analysis can be applied to this spatial aspect of fire service problems.

29
Because response time is an integral factor in saving lives and

reducing property loss, "the objective function" or goal of various

location models is to reduce the time required to reach all demands for

service by the nearest resource to each call. Since buildmg-by-building

or block-by-block identification would yield an excessive number of data

items for the types of computation required, the area under study is

divided into "zones", and response times are calculated from the nearest

fire station to the zone. By comparing the various response times from

actual and potential station locations, it is possible to evaluate the

relative efficiency of different configurations of station locations.

The function of a location model is to determine the "optimum" locational

pattern, where the optimum is defined as the configuration yielding

the minimum average response times.

Two types of location analyses were used to generate and evaluate

alternatives: an adaption of the Maranzana transportation algorithm [5]

and a modification of the REDIST algorithm used to determine voting

districts [6]

.

Both location methods use a heuristic (i.e., a decision- rule that

doesn't guarantee a precisely optimal solution) to determine a "good"

solution at reasonable computer cost. The locational patterns generated

by the Maranzana and REDIST methods were used as two additional

alternatives to be compared with alternatives suggested by the Alexandria

Fire Department through the use of a simulation method to be described in

the next chapter.

5.1 Assumptions

Several assumptions (the first three of which reflect normal fire

service operating procedures) were made in applying the Maranzana and

REDIST models:

1. The important response time is that of the first due engine

company, and it is that response time which should be minimized.

2. Each engine company is assigned to one station at a fixed

location. The company always responds from the station, and is

assumed to be in its station when not servicing calls.

3. A given fire demand zone is served exclusively by the closest

engine company.

4. All alarms occurring within a zone are treated as occurring at

the center of that zone.

5. Travel times from zone centers to each potential station location

are known.

30
A simplified method was used to determine the zones and travel

times in Alexandria. The steps were as follows:

1. Zones were equated with the 1500 x 1500 feet cell divisions

mentioned in Section 3.4.

2. Calls for service within a cell were assumed to originate at

the center of that cell.

3. An (x,y) coordinates system was developed with coordinates (0,0)

at the northwest corner (see Figure 11). For example, the midpoint of the shaded cell has coordinates (0.5, 0.5).

4. The existing fire stations were placed on this coordinate

system as the initial set of locations for the model to improve

upon.

5. The distances between existing and proposed fire station

locations and the centers of the cells were measured along

theoretical streets paralleling the coordinate grid.

6. The travel time from each cell center to each existing and

potential station site was calculated by dividing the

travel distance by the assumed speed of 25 m.p.h.

5 . 2 Maranzana

The Maranzana method consists of the following procedure:

1. Initialize

Make an arbitrary selection from the possible station locations

(in Alexandria, the current configuration).

2. District

Assign each zone to the nearest fire station. A district is

the collection of zones served from a single location. Tf any

zone is equidistant from two or more stations, it is arbitrarily

assigned to one of them.

3. Move

For each district, determine if the current fire station location

minimizes the objective function. If not, determine the location

within that district which does so. This becomes the new fire

station site for that district.

4. Terminate

If the objective function in any district has been reduced,

return to step 2. Otherwise terminate.

31
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'i'\l'l. -;.v.

ll

"'

.i ji - j " 11 i

1 ?u-- m1}

*Ti:

32
The locations selected in Alexandria by the Maranzana solution

method are depicted in Figure 11.

The following equation:

El.t. = W,tn + W.,t + . . . + W t

• 11 11 2 2 nn

where W. is the number of calls from the i-th cell and t. is the travel

time to the i-th cell from the closest fire station, is used by the

Maranzana method as the objective function to be minimized.

This application used 46K of computer core and needed five

passages through Steps 2-4 to terminate. Each such iteration took 40

seconds of computer time on a UNIYAC 1108 with Exec 2 system. Total

running time was 3 minutes and 26 seconds.

5 . 3 REDIST

REDIST uses almost the same objective function. In this case, the

squares of the response times are used in order to make the districting

more compact. However, the model also attempts to balance the work load

(number of calls handled) among the various fire stations. Therefore,

there is a major procedural change.

Steps one and two are the same as in the Maranzana approach.

However, step three is modified to include:

Balance

Redistribute zones to be served from each fire station to equalize

the number of calls handled by each station as much as possible.

The model then continues with step four of Maranzana. The locations and

districts selected by the REDIST solution method in Alexandria are shown in Figure 12 (7)

REDIST ran with 17K of computer core and needed five iterations at 41

seconds per iteration. Total running time was 3 minutes and 35 seconds.

The application of these two methods of locating fire stations

yielded two distinct locational patterns. These patterns are very much

a function of the specific objective function used, the limitations imposed,

and the assumptions made.

It is impractical to experiment by physically relocating fire

stations and observing the results. Therefore, the analytic methods of

Location theory are a valuable managerial tool for discovering reasonable

alternatives to be tested through simulation. The two alternative

locational patterns and the present configuration were compared and

evaluated using the simulation model discussed in the next chapter.

33
M
35
6.0 SIMULATION

Simulation is a very useful tool for analytical management

alternatives and deriving statistics which may be highly relevant to a decision-maker. This technique makes it possible to study the interactions of parts of a given system which may be too complex or too

costly to observe in the real world or to treat by the use of analytical

models. Detailed analysis of output from the simulation model may lead

to a better understanding of the system and to suggestions for improving

it.

Since analysts are forced to seek an appreciation and understanding

of many facets of a system in order to properly develop the model and

write the computer programs , their conclusions are less apt to be

biased by particular inclinations and more apt to be workable within the

system framework. It is also possible to introduce certain informational,

organizational, and environmental changes into the model, and study

their effects on the system operations.

In addition, a simulation model can provide a proving ground and a basis for comparison of results generated by analytical models . For

example, the fire station locations specified by the two location

models in Section 5.0 are evaluated in this section, and the Availability

analysis statistics from Table 8 in Section 4.0 are compared with availability data generated by the simulation model.

6.1 Simulation Model

The simulation model SIM 2, which was applied to Alexandria, is

relatively simple to describe [8] . A fire alarm will be referred to as a case . As simulated time progresses, cases enter the system; i.e., the

fire department receives calls for service. The assignment portion of

the model acts as the dispatcher by determining which particular resources

will service a case. The selected resources then are represented as traveling to the case and remaining at the scene for a specified length

of time. When the designated time elapses, the resources leave the

scene and return to their stations. When the last resource leaves the

scene of the case, that case is terminated.

6

2 Assumptions

The simulation model applied to Alexandria involved various

assumptions

1. Point to point travel times were represented by letting vehicles

travel over a grid system, similar to the cell boundaries in

Figure 10, formed by connecting the cell midpoints. All cases occurring within a cell were assumed to originate at the center

of that cell. Travel speeds were assumed to be 22.5 m.p.h.

when responding to emergency calls, and 15 m.p.h. at all other

times . These speeds were viewed as reasonable by the Alexandria

Fire Department for most of the area to be covered.

36
2. Travel distance from point to point was based on the "metropolitan metric," in which all movement occurs parallel to

the grid-lines, the distance being from the (x,y) location of

the fire station from which resources are dispatched to the

grid coordinates of the center of the cell.

3. As vehicles traveled from point to point on the grid, it was assumed that they traveled the entire distance in the x direction

before traveling in the y direction. A more refined analysis

would use the actual transportation network in Alexandria, and

the speeds possible over each road at the hour the call for

service occurs . Travel times generated in this manner could

be compared to actual runs.

The simplified grid approach was used to permit a faster

evaluation of the possible usefulness of the O.R. tools. The

approximation is quite accurate for the densely populated eastern

area of the city. In the western sector, the speeds are higher

and the road network much sparser, resulting in longer distances

but approximately the same travel times as the metropolitan

metric would indicate. As a result, the simplified approach

offers a first order approximation [9]

4. The time spent on the scene of the alarm was derived from the

data as follows: For each responding company, a time of

notification, t, , and a time back "on the air" (in service), t-,

were available. The travel time was calculated as in steps

1-3. Using a start up time of .77 minutes [10], the on scene

time derived was: t~ - t, - total travel time - .77.

6.3 Simulation Model Input and Output

Required input for the model included, for each case:

1. The day and time the case occurred

2. An identification number for the case, such as its log number

3. The number of additional alarms for the case if more than the

initial response was necessary

4. The location of the case, in (x,y) grid coordinates

5. A number indicating the type of case (public service, accidental

alarm, fire, etc.)

6. The time of alarm, the on scene time, and the number of engine

and truck resources utilized.

The output from SIM 2 consisted of two main parts. The first part

provided a record of the inputs for each case and how the case was handled

by the simulation model (e.g., companies dispatched and response times).

37
The second, major, part of the output consisted o± summary data

divided into six sections:

1. A summary of the simulation specifying:

a. Total number of days simulated

b. Total number of cases serviced

c. Total number of resource hours spent servicing cases

d. Mean average response time per case

e. Number of cases of each type (public service, false alarms,

etc.)

f

.

Average response time of first arriving engine company

g. Average duration of service time for cases of each type

h. Average number of resource hours required for cases of each

type

2. The work load and total time out of its home station for

each individual resource

3. A breakdown of the utilization of the individual resources

measured in resource hours by the day of the week

4. The distribution of responses for the last arriving pumper

for cases where 1 , 2 , . . . , 5 pumpers were dispatched

5. The availability of resources, indicated by the number of

engines idle at any particular time.

The simulation model also printed out the numbers of those cases for

which unusually long response times occurred. These case numbers

may be used to return to the source data to reconstruct the specific

situations involved. This information may suggest ways to modify

dispatch or repositioning policies, or may motivate mutual aid

agreements with neighboring counties in order to reduce the possibility

of such extra- long response times.

The simulation used actual arrival times of alarms, and derived

on-scene times. The availability of engine companies was generated by

checking the number of idle companies every simulated hour throughout

the simulated 123 day period. This availability data was used to

generate availability distributions for each of the three time periods.

The data on engine company availability in period III derived

from the simulation (using the present station locations) is compared

with that from the queueing models in Table 9. There is a close

agreement

.

38
Table 9

Availability Distribution Using

Chaiken and Simulation Models

Probability of (N) Companies Busy

Number of

Companies (N) Simulation Model Chaiken (Availability) Model

.827 .809

1 .099 .107

2 .025 .031

3 .040 .043

4 .007 .006

5 .001 .002

6 .001 .001

7 <0.001 .0002

8 <0.001 .0001

39
6.4 Evaluation of Location Alternatives

The simulation model was used to evaluate several alternative fire

station location patterns , some of which were derived from the models

in Section 5.0 and some of which were suggested by Alexandria officials.

This was accomplished by comparing the operating statistics given by

specific alternatives with those from the actual current configuration of

stations

.

These alternatives were:

1. Optimal location of fire stations as given by the Maranzana

location method

2. Fire station locations as given by the RJBDIST method

3. Add an eighth station in the western part of Alexandria

4. Move the engine company in Station 1 into Station 3

5. Add Station 8; move the engine company currently in Station 1

to Station 3

6. Move the engine company in Station 1 to the new Station 8 location,

For each alternative, statistical distributions were collected

separately for cases where one, two, and three engine companies responded,

as shown in Table 10.

It is desirable to lower both the mean response times and the

standard deviation (.which measures the variability of the responses)

,

by reducing the number of long response times. The differences in Table

10 are not sufficiently large to warrant conclusions without statistical

analysis. Since the Alexandria Fire Department was actually planning

to add an eighth station, further analysis was done on this alternative.

Specifically, the response time statistics from the simulation model

for this case were compared with those for the present station locations.

The distribution of response times for the last arriving engine

produced varying results depending on whether 1, 2, or 3 engines were

used for service.

Figures 14, 15, and 16 graphically show the frequency of different

response times . The two lines are coded with symbols to indicate the

alternative each represents . The two histograms in Figure 14 are close

together over the whole response time range, and no appreciable difference

is observed. However, Figures 15 and 16 show that there were a number of

cases in which the second or third engine company dispatched would arrive

sooner if Station 8 were added.

A standard statistical test (Kolmogorov-Smirnov) was used to

determine if the two alternatives differed significantly. For one and

two engine cases, no significant difference was found. However, three

_

engine cases showed a significant difference at the 1% level of significance. Consequently, it may be concluded that the addition of Station 8

would significantly reduce last-engine response time for cases requiring

three engine companies.
Table 10

Statistics for Different Alternatives

Present Locations

Mean Average

Response Time

(in minutes) Standard Deviation Median

First Engine

Second Engine

Third Engine

2.803

4.807

5.862

1.600

2.901

3.583

2.25

3.75

5.25

Maranzana

First Engine

Second Engine

Third Engine

2.757

4.936

6.214

2.564

2.881

3.771

Redist Locations

First Engine

Second Engine

Third Engine

2.728

4.800

5.928

1.487

2.879

3.839

2.25

4.75

3.75

Add Station 8

2.633

4.447

5.07

1.383

2.875

2.881

First Engine

Second Engine

Third Engine

2.25

3.75

4.25

Move Station 1 to 3

First Engine

Second Engine

Third Engine

2.916

4.736

5.802

1.572

2.924

3.625

2.25

3.75

4.25

Add Station 8,

Move 1 to 3

2.749

4.369

5.011

1.362

2.894

2.914

First Engine

Second Engine

Third Engine

2.25

3.75

4.25

Move Station 1 Station 8

to

First Engine

Second Engine

Third Engine

2.886

4.707

6.002

1.622

2.871

2.602

2.25

3.75

5.25

41
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44
7.0 CONCLUSION

A pilot program was conducted with the cooperation of the Alexandria,

Virginia Fire Department to evaluate the applicability and usefulness of

selected Operations Research methods. These methods, in the form of

computer programs , were modified and adapted to assure that they could

be implemented to provide information which would facilitate fire

department management. In this effort Queueing, Fire Station Location,

and Simulation models were applied to data extracted from the historical

records of the Alexandria Fire Department.

An important aspect of this study is the development of a preliminary

methodology for analyzing certain features of fire service operations

This process consists of the following four steps

(1) Data Analysis - collection and evaluation of historical data

(2) Availability Analysis - use of Queueing theory to determine

probable demands for service

(3) Location Models - use of response times over a street network

and fire service demand factors in an objective function to

determine alternative fire station location configurations

(4) Simulation Model - use of a computer based model to compare

various alternatives and to test results of the Availability

Analysis and Location Models.

It is hoped that the information provided by this methodology may

facilitate better management decisions based on a more complete understanding of the mechanisms involved in furnishing fire service for an

area.

The simulation model used in Alexandria does not currently include

provisions for such factors as:

1. Queueing of cases by the dispatcher

2. Delayed response time when resources are occupied

3. Interruption of "low priority" service when an urgent case occurs

4. Temporarily transferring resources into other depleted stations

when necessary.

These provisions, although obviously important in modeling some fire

departments, were not necessary in Alexandria because of the high degree

of availability. However, the simulation model was purposely developed

with a modular structure to facilitate adding such provisions as needed

to adapt the model to apply to other fire departments.

The authors would like to express their appreciation for the

cooperation of Chief Milton T. Penn and Fire Protection Engineer

William H. Everard of the Alexandria, Virginia Fire Department. Without

their valuable guidance this study would not have been possible. We

45
also wish to acknowledge the considerable technical input and assistance

of our colleagues Donald Coiner, Patsy B. Saunders, and Arnold L. Weber.

We are indebted to Dr. John Rockett of the National Bureau of Standards

for providing financial assistance for this project through the NBS

Fire Research Program. Finally, we wish to express our gratitude to

Marilyn Taylor for long hours spent in preparation of the manuscript.

-\

46
REFERENCES

[1] Churchman, Ackoff, Arnoff, Introduction to Operations Research

(New York: John Wiley and Sons, Inc. , 1957) , p. 18.

[2] Edward H. Blum, "Fire Service: Challenge to Modern Management,"

Public Management , Nov. 1970.

[3] For a description of the specific mathematical processes involved,

see James Fortune, Jr. and Joseph A. Swartz, Jr., "Availability

Analysis as a Fire Service Management Tool," unpublished NBS

report

[4] Jan M. Chaiken, "The Number of Emergency Units Busy at Alarms

with Require Multiple Servers," New York City Rand Institute,

R-531, March 1971.

[5] F. E. Maranzana, "On the Location of Supply Points to Minimize

Transport Costs," Operational Research Quarterly , XV (1964), 261-270,

[6] Crond, Inc., Redist 5.3 Program Description and User Manual , 1969.

[7] For a more technical analysis of the procedures described in this

section see Arnold Weber, Documentation of LOC Models , unpublished

NBS report.

[8] Patsy B. Saunders, "A Computer Model for Simulating the Response

Activities of a Fire Department," NBS Report 10 488, Sept. 1971.

19] For further explanation of using such a metric in a metropolitan

area, see J. M. Burt and J. S. Dyer, Working Paper #6, EMS-70-6-W,

August 1970, Emergency Medical Systems Project, UCLA Graduate

School of Business.

10] The start up time was taken from J. L. Bryan and R. P. Thornberry,

"The Development and Evaluation of a Systematic Analysis Procedure

for Selection of Fire Station Sites in Prince George's County,

Maryland," Unpublished paper, Fire Protection Curriculum, University

of Maryland, July, 1970.

47
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLIC ATION OK REPORT NO. NBS-TN-782

2. Gov't Accession

No.

4. TITLE AND SUBTITLE

Application of Systems Analysis to the Operation of a Fire

Department

3. Recipient's Accession No.

5. Publication Date June 1974

6. Performing Organization Code

7. AUTHOR(S)

Ernst K. Nilsson, Joseph A. Swartz, and M. Westfall

8. Performing Organ. Report No

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

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Same as No. 9.

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Library of Congress Catalog Card Number: 74-600079.

16. ABSTRACT (A 200-word or less (actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Rising labor costs and increasing competition for tax dollars to provide urban

services demand that a more precise methodology be used in the management of fire

departments. A pilot program was conducted with the cooperation of the Alexandria,

Virginia Fire Department to evaluate the applicability and usefulness of selected

Operations Research tools. These tools, in the form of computer models, were

modified and adapted to assure that they could be implemented to provide information

which would facilitate fire department management. In this effort queueing,

facility location, and simulation models were applied to sample data extracted from

the historical records of the Alexandria Fire Department. It was established that

such models do provide valuable information which may assist managerial decisions.

This paper describes the city of Alexandria and its fire department, the O.R. models

output from their application, and evaluations of the output.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Alexandria; fire department; location; operations research; resource allocation;

simulation; systems analysis.

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