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A GPSS -FORTRAN CASE STUDY by Charles Joseph Petronis

A GPSS -FORTRAN CASE STUDY by - CORE · H.STORAGEREQUIREMENT FORTRAN GPSS Comparison REPLICATION FORTRAN GPSS Comparison DATACOLLECTIONANDDISPLAY FORTRAN GPSS 3. Comparison V. CONCLUSIONS

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Page 1: A GPSS -FORTRAN CASE STUDY by - CORE · H.STORAGEREQUIREMENT FORTRAN GPSS Comparison REPLICATION FORTRAN GPSS Comparison DATACOLLECTIONANDDISPLAY FORTRAN GPSS 3. Comparison V. CONCLUSIONS

A GPSS -FORTRAN CASE STUDY

by

Charles Joseph Petronis

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LIBRARY „_«,NAVAL POSTGRADUATE SCWOB

MONTEREY. CALIF. 93940

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INTERNALLY DISTRIBUTED

RFPflRT

United StatesNaval Postgraduate School

THESISA GPSS-FORTRAN CASE STUDY

by

Charles Joseph Petronis

April 1970

Tku document hcu> bten appnjovtd ^oK pubtcc k<l-

tzcu>z and Acute.; i£i> dLUtsubtxtloYi <U unJUmittd,

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A GPSS-FORTRAN Case Study

INTERNALLY DSSTRiBUTEDby

RE!

Charles Joseph Petronis

Major, United States ArmyB.S., Norwich University, 1960

Submitted in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE IN OPERATIONS RESEARCH

from the

NAVAL POSTGRADUATE SCHOOLApril, 1970

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CI

ABSTRACT

The objective of this study was to compare two commonly used

computer simulation languages: GPSS and FORTRAN. The comparison

was made by simulating an identical system in both languages. The

comparison criteria used to evaluate the languages were as follows:

ability to represent system, simulation time, ability to represent

stocastic phenomena, programming time, computer running time, monitor-

ing and debugging, storage requirements, data initialization and starting

conditions, replication, data collection and display. The results from

this study indicated that a system may be modeled four to five times

faster using GPSS as compared to FORTRAN. The modeled system was

simpler to conceptualize in GPSS, and the model required reduced pro-

gramming, debugging and monitoring time compared to the FORTRAN

model

.

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JBRARY -

AVAL POSTGRADUATE SCHOOlfONTEREY,, QALIF. 93940

TABLE OF CONTENTS

I. INTRODUCTION 9

II. LANGUAGE COMPARISON CRITERIA 11

A. ABILITY TO REPRESENT SYSTEM 11

B. SIMULATION TIME 12

C. ABILITY TO REPRESENT STOCASTIC PHENOMENA 12

D. PROGRAMMING TIME AND COMPUTER RUNNING TIME 13

E. MONITORING AND DEBUGGING 13

F. DATA INITIALIZATION AND STARTING CONDITIONS 14

G. STORAGE REQUIREMENTS 15

H. REPLICATION 15

I. DATA COLLECTION AND DISPLAY 16

III. THE MODEL 17

A. TORN TAPE RELAY CONCEPTS 17

B. SYSTEM MODELED 19

C. FORTRAN SYSTEM MODEL 22

D. GPSS SYSTEM MODEL 3

IV. GPSS> -FORTRAN COMPARISON 3 6

A. ABILITY TO REPRESENT SYSTEM 3 6

1. FORTRAN 3 6

2. GPSS 37

3. Comparison 38

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B. SIMULATION TIME 38

1. FORTRAN 38

2. GPSS 39

3. Comparison 39

C. ABILITY TO REPRESENT STOCASTIC PHENOMENA 40

1. FORTRAN 40

2. GPSS 40

3 . Comparison 41

D. PROGRAMMING TIME 42

1. FORTRAN 42

2. GPSS 42

3. Comparison 42

E. COMPUTER RUNNING TIME 43

1. FORTRAN 43

2. GPSS 44

3. Comparison 44

F. MONITORING AND DEBUGGING 45

1. FORTRAN 45

2. GPSS 46

3 . Comparison 47

G. INPUT DATA AND INITIALIZATION 47

I • FORTRAN 47

2. QPS8 48

li, rin mi 48

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H. STORAGE REQUIREMENT

FORTRAN

GPSS

Comparison

REPLICATION

FORTRAN

GPSS

Comparison

DATA COLLECTION AND DISPLAY

FORTRAN

GPSS

3 . Comparison

V. CONCLUSIONS

APPENDIX A

APPENDIX B

APPENDIX C

Exogenous Data

FORTRAN Computer Model

Explanation of Arrays and Subroutines

FORTRAN Flow Chart

FORTRAN Computer Program

GPSS Computer Model

GPSS Flow Chart

GPSS Computer Program

BIBLIOGRAPHY

INITIAL DISTRIBUTION LIST

FORM DD 1473

49

49

49

50

50

50

51

51

52

52

52

53

55

57

66

66

74

108

124

125

137

146

148

149

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LIST OF ILLUSTRATIONS

Figure Page

1 . TORN TAPE RELAY NETWORK 20

2. ARRAY FF(5, 10, 3) 23

3. A FORTRAN FLOW CHART 2 7

4. A GPSS FLOW CHART 39

5. TERMINAL 1 PERCENT PEAK LOAD ARRIVAL RATE 58

6. TERMINAL 2 PERCENT PEAK LOAD ARRIVAL RATE 59

7. TERMINAL 3 PERCENT PEAK LOAD ARRIVAL RATE 60

8. TERMINAL 4 PERCENT PEAK LOAD ARRIVAL RATE 61

9. TERMINAL 5 PERCENT PEAK LOAD ARRIVAL RATE 62

10. PERCENT TRAFFIC TRANSMITTED TO EACH TERMINAL 63

11 . MEAN PEAK HOUR ARRIVAL RATE BY PRECEDENCE 64

12. MEAN MESSAGE TRANSMISSION TIME BY PRECEDENCE 65

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ACKNOWLEDGEMENT

The author wishes to express sincere appreciation to Professor

Alvin F. Andrus for supervision, encouragement and for the many sug-

gestions that materially added to this study.

The author especially wishes to thank his wife, Bunny, and

daughters, Debra, Susan, and Karen for administrative assistance

and for the many sacrifices they made during the writing of this thesis

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I. INTRODUCTION

Computer simulation has become an ordinary and useful technique

of the operations analyst. In industrial and military operations research,

complex as well as simple systems are being simulated by computer for

both educational and analytical purposes. In an effort to reduce both

the amount of detailed programming required and the amount of intricate

simulation methodology that must be known in order to create a computer

simulation, several special purpose simulation languages have been made

available to the operations research community [Ref s . 15, 16, 17]. Prior

to the introduction of these simulation languages, computer simulation

programs were restricted to either the available assembly or compiler

languages. It is not clear, however, that the task of simulating a system

is always simpler when using a simulation language.

It is obvious that as a computer language becomes specialized, it also

becomes restrictive. It is also possible that an increase in speciali-

zation for a computer language will tend to decrease the efficiency of

the language in terms of running time and allocated memory space. Moti-

vated by these thoughts, the objective of this thesis is to compare the

usefulness of two very common programming languages: GPSS and

FORTRAN. GPSS is a specialized simulation language for the simulation

of queueing problems and FORTRAN is a general purpose language. A

detailed description of these languages is not contained in this thesis

but may be found in Ref s . 3 , 4 , 6 , 7 , 8 , and 14 .

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The comparison of GPSS and FORTRAN in this thesis is made by

simulating an identical queueing system in each of these languages.

For the queueing system simulated, identical assumptions were made

relative to modeling the system and the same exogenous data was used,

Models in each of the languages provided comparable output data. At

the beginning of this study, the author was equally familair with each

language. Based upon these two simulations, the languages were then

relatively evaluated according to the following criteria:

1 . Ability to represent system

2 Simulation time

3. Ability to represent stocastic phenomena

4. Programming time

5 . Computer running time

6. Data initialization and starting conditions

7 . Storage requirement

8 . Replication

9. Monitoring and debugging

10. Data collection and display

These criteria are discussed in Chapter II in light of their importance

to simulation model building.

It should be made clear that the content of this thesis is directly

related to a comparison of GPSS and FORTRAN in programming a simple

queueing situation. No attempt is made to compare these languages

beyond their application in programming this sample problem.

10

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II. LANGUAGE COMPARISON CRITERIA

The criteria used to compare FORTRAN and GPSS represent both the

economic considerations of choosing a language as well as the desirable

features of a simulation language. The economic considerations [Ref. 12,

pgs. 240-241] relate to cost and availability. Cost can be equated to

the man hours required to obtain a validated computer model, together

with the computer operating time required to obtain the final results.

Availability includes the availability of computer hardware as well as the

availability of knowledgeable programmers and technicians. The desirable

features of a simulation language [Ref. 9, pgs. 26-38] are qualities that

assist the programmer in conceptualizing, programming, debugging and

experimenting with the computer model. A detailed explanation of the

specific criteria utilized to compare FORTRAN and GPSS follows.

A. ABILITY TO REPRESENT SYSTEMS

Most systems of interacting entities can be said to possess two

structures: static and dynamic. The static structure is independent of

time, and consists of the framework or structure within which action

takes place. The dynamic structure is time dependent and includes the

processes and actions that occur within the static structure of the model.

In order to simulate a system, it is, therefore, important that the

language used must contain an inherent framework or flexibility so that

both the dynamic and static structure of the system can be easily and

realistically included in the simulation. As examples of the two structures,

11

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consider the operation of a message center. The transmitters, receivers,

and electrical circuits represent the static structure. The arrival and

departure of messages over the circuits make up the dynamic structure

for this system

.

B. SIMULATION TIME

In order to simulate the dynamics of a system, a method is needed

which portrays the passage of time. Time in a simulation is controlled by

means of a computer clock which is a programming mechanism that approxi-

mates the continuous flow of time in the simulation. Clocks are of two

basic types: fixed time and next event. Fixed time clocks operate by

advancing simulated time in discrete time intervals. At the completion

of each time interval, a control mechanism scans all the possible actions

that may take place and all computation scheduled for this interval is

performed. The clock then advances into the next interval and the

scanning process is repeated. Next event clocks utilize a control device

that, at the completion of an event or computation, advances simulated

time directly to the time of the next event scheduled to occur. For a

detailed description of these clock mechanisms see Naylor [Ref. 12].

C. ABILITY TO REPRESENT STOCASTIC PHENOMENA

Events in the real world usually do not occur with regularity or

according to some fixed pattern. The variability and uncertainty with

which events occur are most often described by means of probability

statements and distributions, e.g. , event A has fifty percent chance of

12

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occurring, or event B will occur every ten days plus or minus three days.

To include these probability statements and distributions, a method is

needed within the dynamic structure of the model to generate random

numbers. Random numbers used in conjunction with probability distri-

butions and statements are used to determine the outcome of stocastic

events, e.g. , did event A occur or not? In order to adequately model

real world systems, it is therefore necessary to include in the evaluation

of any computer language the ease with which the variability and un-

certainty of events can be included in the simulation.

D. PROGRAMMING TIME AND COMPUTER RUNNING TIME

For any simulation, programming time and computer running time

are important considerations. Both times represent dollars and, there-

fore, must be considered prior to choosing a computer language. Complex

languages which compile and execute slowly in comparison to simpler

languages may greatly reduce programming time due to their syntax. In

deciding on a language to use, a cost and time trade off analysis should

be made. This analysis can quite often only be made empirically, i.e. ,

by comparing the results of the different languages as is being done in

this thesis .

E. MONITORING AND DEBUGGING

An essential requirement for any programming language is that it

ought to provide features that assist the programmer in debugging syntax

and logic errors. For simulation languages in general, three desirable

13

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debugging features are:

1 . A list of compilation and execution errors referenced by

statement number and clock time.

2 . A list of execution errors reported with a complete printout

of the status of the program at the time of error. This print-

out should contain as a minimum: clock time, status of

appropriate variables and related parameters from the sub-

routines currently in effect

.

3 . A trace back feature which would provide some method to

trace a given event thru the system.

These three features are also necessary in order to monitor the system

dynamics. Without the ability to trace an event and the ability to

observe the system at various times, many logic errors would be im-

possible to locate [Ref. 10, pgs. 35-36].

F. DATA INITIALIZATION AND STARTING CONDITIONS

Simulation studies often use extensive exogenous data. Therefore,

convenient methods to initialize exogenous data into the computer model

is a desirable language feature. Once the model has been initialized,

the immediate objective then becomes to obtain information about the

system at various points in time. In the analysis of some systems, the

analyst may decide to study the system during steady state conditions,

while for other systems, the transient conditions may be more important.

Another desirable feature for comparison of language is then the ease

14

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with which the inherent structure of the language allows the analyst to

drive the simulation to a steady state condition. This must include, of

course, a convenient method for minimizing the amount of execution time

required to arrive at a steady state condition.

G. STORAGE REQUIREMENTS

Computer core storage is fixed for each model computer. This re-

stricts the capability of each model computer to perform jobs within its

memory capacity. In order to obtain the most efficient use of a computer's

memory capacity, many computer facilities encourage programs to be

written with small storage and time requirements by providing quicker

turn around times to these programs . The language storage requirement

therefore becomes important in obtaining shorter turn around times during

the debugging and experimentation phase of the simulation. Core storage

requirements of a computer language can therefore materially affect the

time required to project completion.

H. REPLICATION

When simulation results are put to the test of statistical analysis,

it is of primary interest to obtain results with a specified degree of

confidence. In order to be able to specify a degree of confidence, a

number of observations of the experiment must be obtained. These

observations are obtained by replicating the computer experiment the

desired number of times. The ease with which program replications can

be made is therefore a measure of contrasting two simulation languages.

15

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I. DATA COLLECTION AND DISPLAY

Data collection is a necessary requirement for any simulation.

Ideally, data collection should be automatic, but in any event, data

collection statements should not interfere with the operations of the model.

Since completely automatic data collection is not practical, the next best

alternative is to have certain information automatically collected and the

remaining information available at the discretion of the programmer. The

following data should be available as output at little or no inconvenience

to the programmer [Ref. 10, pgs . 32-34].

1 . The number of observations and the maxima and minima for

all variables

2 . Sums and sums of squares for time independent variables

3. Time-weighted sums and sums of squares for time-independent

variables

4. Variable value histograms for time-independent variables

5. Time-in-state histograms for time-dependent variables

6. Time series plots over specified time intervals

The recording of results is a primary objective in every study.

Therefore, the language selected for simulation should allow for varying

output formats that are dependent upon the programmers needs. However,

as is the case with data collection statements, the programmer should not

have to spend a great deal of time in writing or debugging output data

statements

.

16

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III. THE MODEL

This chapter introduces the torn tape relay network concept of

operation in Section A and describes the system that was simulated for

this case study in Section B. The FORTRAN and GPSS models of the torn

tape relay network are described in Sections C and D respectively. The

FORTRAN and GPSS programs are discussed with the intent of providing

the reader insight into the methods that can be used by a programmer to

simulate the static and dynamic structure of a system.

A. TORN TAPE RELAY CONCEPT

The purpose of a torn tape relay network is to move message traffic

from an origin to a destination within the network. A typical torn tape

relay system consists of a number of terminal and relay stations con-

nected by circuits. A terminal originates and terminates messages for a

military headquarters. Messages originated at a terminal are translated

into a coded perforated tape. The perforated tape code is then transmitted

to a relay station according to the assigned precedence and desired routing

of the message. A relay station is typically connected to many terminal

stations in the geographical area as well as to other relay stations. The

mission of a relay station is to accept messages from the supported

terminals and connecting relays and to retransmit the messages to the

next station according to the messages routine instructions. This next

station may be another relay or a supported terminal station.

17

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A message may be assigned one of four precedences. Listed in

order of importance from high to low, these precedences are: flash,

immediate, priority, and routine. All messages are transmitted from one

station to another on a first in first out, FIFO, discipline ordered by

precedence. When a flash message is received at a station and no

circuit is free to the next station in accordance with the routing instruct-

ions, a lower precedence message occupying a transmitting circuit is

pre-empted. The flash message is then transmitted over the pre-empted

circuit and the pre-empted message is refiled according to its original

receipt time. The pre-empted message is then eventually retransmitted

according to the normal FIFO discipline. A message with a flash pre-

cedence is the only type of message with pre-empting authority.

Prior to reaching the final destination, messages often remain in

queue at some station and are said to be backlogged. Station backlogs

are computed to be the time required to transmit all messages in queue

for a given station. The total backlog is often separated into two

categories: a high precedence message backlog consisting of flash and

immediate messages and a low precedence backlog consisting of routine

and priority messages. Backlog statistics are used as a measure of

effectiveness to evaluate a station's ability to pass traffic.

The number of circuits interconnecting two stations regulates the

backlog that exists between these stations. Additional tape transmitters,

receivers, and personnel to operate the equipment are also needed as the

number of circuits increase. The additional circuits, equipment and

18

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personnel can be equated to dollars. Hence, in designing or operating a

torn tape relay, one attempts to minimize the cost of operation by mini-

mizing the number of interconnecting circuits, subject to some fixed

effectiveness criterion. The maximum backlog that will be tolerated is

often used as the fixed effectiveness criterion.

B. SYSTEM MODELED

The torn tape relay network that was modeled for this study con-

sisted of five terminal stations and one relay station. A diagram of the

system simulated is depicted in Figure 1. The terminal stations are

numbered 1 , 2 , 3 , 4 and 5 . The relay consisted of five bays and are

labeled 6, 7, 8, 9 and 10 in the diagram. Each bay contained relay

equipment used to transmit and receive messages to a given terminal.

The circuits interconnecting the terminals and relay bays are represented

by directed lines in the diagram. Transmitting circuits are indicated by

the direction of the arrow.

The five terminal stations and five relay transmit bays together

with the associated circuitry comprised the static structure of the system

The dynamic structure of the system consists of messages possessing a

given precedence, arrival time, message length and destination moving

thru the static structure .

The problem addressed in this study was to simulate the torn tape

relay network represented in Figure 1 and to determine the minimum

number of circuits required between stations consistent with acceptable

19

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TORN TAPE RELAY NETWORK

(ter*\n*l\

/tcrhiamlA

TERfMN^W.

D

/^ti^in^

Figure 1

20

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backlog figures. Backlogs were considered excessive if low precedence

messages were backlogged in excess of 15 minutes and high precedence

messages in excess of 2 minutes .

Various operating characteristics for all the stations were assumed

for the system. These characteristics included probability distributions,

message density functions, peak load figures and average message

length. The following assumptions were used in modeling the torn tape

relay network:

1. All messages introduced into the system reached the desired

destination and no messages were misrouted.

2 . Message center record keeping procedures did not contribute

to backlog figures .

3 Circuit outages were not considered; hence, all circuits

experienced one hundred percent reliability.

4 . The time between message arrivals for each precedence

message was distributed exponentially with mean peak hour

values as listed in Figure 11, Appendix A.

5. The peak hour arrival rate was dependent upon time of day

and was different for each site. The peak hour arrival rates

utilized are listed in Figures 5 thru 9, Appendix A.

6. The average message length was not time dependent, but was

dependent upon the station and precedence of the message.

Message length was assumed exponential with mean values

as listed in Figure 12, Appendix A.

21

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C. FORTRAN SYSTEM MODEL

FORTRAN is a general purpose language, GPL, in that the language

was not designed for special purpose applications such as simulation.

FORTRAN is a comparatively simple language to learn, because the symbols

and mnemonics are analogous to those of mathematics. For this reason,

and due to the FORTRAN compilers universal availability, the language

became a common computer language for scientific computations.

FORTRAN makes use of variables, subscripted variables, constants,

expressions and functions. The number of different functions or sub-

routines used by a programmer is limited only by the size of the computer

available. For simulation programming using FORTRAN, the programmer

has great flexibility by being able to write a general main program con-

taining a timing clock., and then calling various subroutines for execution.

In order to model the static structure of a system in FORTRAN, one

must portray the structure of the system using the subscripted-unsub-

scripted variables and constants in conjunction with FORTRAN functions

and expressions. The dynamic structure of a system is represented in

FORTRAN by altering the flow of statement execution in a manner that

reflects the action occurring in the actual system. The order of state-

ment execution is varied in FORTRAN by use of IF statements, COMPUTED

GO TO statements and logical type statements.

In order to simulate the torn tape relay network in FORTRAN, the

static structure was represented by subscripted arrays. Four three

dimensional arrays, namely RR (i, j , k) , PP (i, j , k) , OO (i, j , k) and

22

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Di*\&to*>K>h) </

CD

cn•rH

P-4

23

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FF (i,j ; k), were used to store information pertaining to routine, priority,

immediate and flash messages, respectively. Figure 2 contains a repre-

sentation of the FF array. The k dimension of each array was equal to

three, and was used to store the arrival time, required transmission

time, and destination of each message waiting for transmission at the

terminals and relay transmit bays. The i and j dimension of these arrays

fixed respectively the number of messages and the station at which the

messages were currently located. The j dimension was equal to ten with

argument one thru five corresponding to the five terminals and arguments

six thru ten corresponding to the five relay transmit bays. The arguments

of the j dimension corresponded to the station numbers depicted in

Figure 1

.

The d eimension was different for each precedence array and was

selected to permit at least a thirty minute backlog of messages to exist

for each precedence category at each station. For k equal one, message

arrival times were stored in the i dimension in increasing order.

Ten one dimensional arrays HOLDl(i) thru HOLDlO(i) were used to

represent the circuits between terminals and relay bays. The arrays

HOLD1 thru HOLD10 correspond to the numbering of Figure 1; these

arrays contained the time at which a specified circuit would be free.

The number of transmit circuits from one location to another was equal to

the dimension of the HOLD array corresponding to this pair of stations.

The dynamic structure of the system was represented by moving

message parameters from the terminal storage areas represented by

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position 1 thru 5 of the j dimension to the desired relay transmit bay

represented by position 6 thru 10 and then from the relay to the desired

destination. The order of statement execution was controlled by a FORTRAN

COMPUTED GO TO statement that acted as a next event clock. Program

control was transferred to the station that had the highest precedence

message with the lowest arrival time available for transmission. A

message was available for transmission if the scheduled message arrival

time was less than or equal to the simulation clock time and there was a

free circuit in order to transmit the message to the connecting station.

Transmission from a terminal was accomplished by transferring message

parameters from the array column representing the terminal to the array

column representing the relay transmit bay that will transmit the message

to its final destination. In addition, the message transmission time is

added to current simulation time and this value is placed in the proper

HOLD array.

For example, suppose a flash message from terminal two to terminal

three was selected as the next event in the simulation. Since relay

transmit bay eight transmits to terminal three, the message parameters

from column two would be transferred to column 8 of array FF. The

arrival time of the message for terminal eight would also be updated by

the transmission time of the message. In addition, the time at which

transmission ends would be transferred to HOLD2(i).

The information was deleted from the HOLD array after the required

message lapse time by use of the next event clock. Each time a set of

25

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message parameters was transferred from a terminal column, the remaining

message parameters moved forward one position, and a new set of message

parameters was created to occupy the empty position. After the creation

of a new message, all positions in the j dimension column were filled,

and the message arrival times were in ascending order. Once a message

was transferred to a relay transmit bay column, the message arrival

times in the column were not necessarily in ascending order. Hence,

after a message was transferred to a relay transmit bay column, all

message parameters in the column were ordered to insure the lowest

arrival time message was in position one and therefore was the next

scheduled message to be transferred from the column.

Messages in a relay transmit bay column selected as the next event

were processed in a similar manner. The single exception being that

messages transmitted by the relay were destined for the final destination.

Hence, after a message was held in the respective HOLD array for the

messages transmit time, the message attributes were destroyed. The

destruction of the message's parameters represented the successful

delivery of the message.

Backlogs were computed after transferring a message to the next

station. A message was backlogged if simulation time was greater than

the message arrival time stored in the j dimension of the respective

precedence array. All messages stored in relay terminal bay columns

were backlogged, whereas, only the messages with arrival times less

than clock time were backlogged in the terminal columns. The messages

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FORTRAN FLOW CHART

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27

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LXreft*

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28

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r^ofe

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29

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with times greater than the clock time in the relay columns were future

events and had not yet been introduced to the model. The backlog for a

station was computed by totaling message time lengths for those messages

with arrival time less than or equal to clock time. The maximum backlog

that occurred during a computer run was recorded for each terminal station

and relay transmit bay.

A flow chart of the torn tape relay network in FORTRAN logic is

illustrated in Figure 3. This is an abbreviated flow chart and includes

only the main program and the programmed operation of a terminal. Al-

though some detail is omitted, Figure 3 portrays a system flow chart

for FORTRAN. A complete flow chart of the FORTRAN model is included

in Appendix B, together with an explanation of the symbols, and descrip-

tion of the arrays and subprograms used.

D. GPSS SYSTEM MODEL

General Purpose Simulation System, GPSS, is a popular simulation

programming language. GPSS was designed to be used as a simulation

language and as such makes special features available to simulation

programmers. These features hopefully reduce the time required to

simulate a system by reducing problem formulation time, programming

time and debugging time. GPSS was designed by the International

Business Machines Corporation and is well documented.

GPSS uses a block diagram flow chart procedure to represent the

static structure of a system. The blocks used to represent the static

structure are divided into six categories. The most fundamental of

30

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these categories contain the GPSS entities STORAGES, FACILITIES and

LOGIC SWITCHES. These entities are the building blocks of GPSS. A

FACILITY allows entry to only one transaction at a time. A transaction is

a dynamic entity and is used to represent movement in the system. The

length of time a FACILITY is occupied by a transaction may be determined

by a transaction's parameter value. A parameter describes a particular

transaction attribute. STORAGES allow entry to several transactions

simultaneously. LOGIC SWITCHES are two position gates which alter

transaction flow according to the status of some other entity or trans-

action parameter value. The dynamic structure of a system is modeled

in GPSS by the use of transactions. Transactions are created and

destroyed as needed during the computer simulation. Transactions may

have associated with them a set of parameters. The values assigned to

these parameters remain with the transaction until they are changed or

the transaction is deleted from the model

.

Associated with GPSS entities are certain standard numerical

attributes. The value of these attributes may be referred to or collected

by the programmer during the execution of the program. Standard

numerical attribute values may be used to trigger LOGIC SWITCHES,

assigned to transaction parameters, as well as stored for future use.

For the torn tape relay network, the terminal and relay sites,

transmitters, receivers, and interconnecting circuits were modeled by

use of a block diagram. The messages were represented by transactions

which moved through the block diagram according to the instructions of

31

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the model. Transactions were created in the model for each precedence,

and from each terminal according to an exponential distribution. The

intermediate and final destinations, precedence, and message length

were assigned to transaction parameters in the torn tape relay model.

Extensive use was made of the FACILITY entity. FACILITIES were

used to represent torn tape transmitters . Transactions waited in and

advanced in queue according to the FIFO discipline. A transaction

occupied a facility, for the simulation time length of the message. A

PREEMPT block allowed transactions representing flash messages to

pre-empt a FACILITY occupied by a lower precedence transactions.

Entities may be referred to by indirect addressing in the GPSS

program. Normally, each entity is designated by number or mnemonic

in the flow chart of the system. However, it is also possible to

designate a particular entity by the value of a transaction parameter.

Indirect addressing is often used to specify entity numbers when there

are several identical processes occurring in the system to be modeled.

In the torn tape relay model, five terminals and five relay trans-

mitter bays performed identical operations. Each location transmitted

messages according to the FIFO discipline. The terminals transmitted

to the relay, and each relay transmitter bay transmitted messages to a

particular terminal. Therefore, since the functions at each location

were identical, the required programming was reduced tenfold by in-

corporating indirect routing for referencing most entity blocks.

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A flow chart in GPSS of a single terminal is depicted in Figure 4.

This flow chart differs slightly from the actual GPSS model used in that

indirect routing, statistic gathering and storage of transactions in user

chains is omitted. A complete flow chart of the model is included in

Appendix C together with an explanation of symbols used. A comprehensive

discussion on GPSS may be found in IBM manuals and Schriber [Refs. 6-8,14]

33

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GPSS FLOW CHART

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34

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9^e. Pl^-erA^T

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VALUES /^ TABLES

35

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IV. GPSS-FORTRAN COMPARISON

GPSS and FORTRAN are evaluated in this chapter using the criteria

discussed in Chapter II. The evaluation is based upon observations and

experiences encountered while modeling the torn tape relay network dis-

cussed in Chapter III.

A. ABILITY TO REPRESENT SYSTEM

1. FORTRAN

The torn tape relay network was first simulated in GPSS and

then in FORTRAN. The author was hence quite familair with the system

prior to programming the system in FORTRAN. Even so, a considerable

amount of time was consumed trying to conceptualize the problem in the

form of subscripted-unsubscripted variables . Many methods proved

infeasible due to the requirement to record backlog statistics and due

to the pre-empt authority of flash messages.

In order to collect backlog statictics, backlogged messages

were simulated by creating messages in advance with a scheduled time

of arrival. When simulation time advanced and equaled the arrival time

of a message, if a circuit was available to the desired destination then

the message was transmitted. If a circuit was not free, the message

would wait in queue and be processed according to the FIFO discipline.

The only practical method to store messages waiting for an available

circuit, appeared to be to store the message parameters in arrays. Since

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arrays were used, the following decisions had to be made before a system

static structure could be formulated:

1. How should message parameter values be assigned to

arrays?

2 . How many arrays and what dimensionality should be

used?

3. What properties for each message should be retained?

4. How is information to be exchanged between arrays

in order to represent the dynamic structure of the

system?

2. GPSS

The torn tape relay network was comparatively simple to

represent in GPSS. The system static structure was logically represented

by means of a GPSS block diagram similar to Figure 4 of Chapter III. The

blocks FACILITY, STORAGE, TRANSFER, QUEUE and PREEMPT readily

portrayed the realistic operation of the system. Once the entire block

diagram was completed, the programming of the model in GPSS followed

directly, since there exists a one to one correspondence between GPSS

blocks and GPSS program statements. The dynamic structure of the torn

tape relay problem was represented in GPSS by GPSS transactions. For

this problem, transactions were considered messages. Transactions

were created at prescribed interarrival rates and assigned parameter

values corresponding to precedence, message length and destination.

The flow of transactions followed the block diagram structure of the

network

.

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3 . Comparison

The torn tape relay network system was much easier to

represent in GPSS than in FORTRAN. The construction of the GPSS block

diagram using the block mnemonics facilitated building a GPSS model of

the system. Initially the system was difficult to conceptualize using

FORTRAN statements since it was possible to become involved in the

details of FORTRAN and lose presence of the system to be modeled. The

flexibility of modeling a system in FORTRAN can be a handicap for less

experienced programmers because a programmer must select from among

apparent alternate methods of structuring the model. Hence, it can be

difficult and time consuming to determine which methods are feasible

and which feasible method is best.

B. SIMULATION TIME

1. FORTRAN

The incremental time clock and the next event clock were

considered for use in the FORTRAN model. The incremental time clock

was not used, however; this clock appeared to be simple to utilize but

did not appear very efficient since simulation time would be advanced

in increments of one second and many hours of operation had to be

simulated. The next event clock was used and appeared to be more

ficient since simulation time is advanced directly to the time of the

Kt event

.

In retrospect, the Incremental clock might have been a more ef-

ficient choice, since time progressed in small time increments in the

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model. If an incremental clock had been used, FORTRAN bolean variables

could have been incorporated in lieu of the FORTRAN IF statements and

the COMPUTED GO TO statement. Bolean variables associated with each

possible event could have been set to a go condition if the event was

scheduled to occur during the next time increment. Bolean variables

require considerably less computer time and hence might have resulted

in a more efficient time clock .

2. GPSS

The timing mechanism of GPSS was a next event clock. The

GPSS program operated by moving transactions thru a block structure

that represented the static structure of the system. Each block repre-

sented the possible occurrence of an event in the system. The GPSS

master program maintained a record of when these events were scheduled

to occur and processed the events in their proper sequence in time.

3 . Comparison

The most important difference in comparing GPSS and FORTRAN

with respect to simulation time is that GPSS has a built in timing clock

and FORTRAN does not. When using GPSS the simulation of a system

must include the next event clock. However, no programming or struct-

uring of this clock mechanism is required since the clock feature of

GPSS is entirely automatic within the block structure. The simulation

of a system in FORTRAN does require the programming and structuring of

a clock mechanism to meet the specific needs of the system being

simulated.

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C. ABILITY TO REPRESENT STOCASTIC PHENOMENA

1. FORTRAN

The mathematical structure of FORTRAN facilitated the pro-

gramming of probability distributions, functions and functional relation-

ships . Many useful mathematical functions are available directly from

the FORTRAN library. In addition, subroutines are available to generate

random numbers and variates from most of the ordinary theoretical

probability distributions. Variates can also be easily generated from

empirical distributions, see Naylor [Ref. 12].

Random numbers were generated in the FORTRAN torn tape

relay model using a library subroutine. The inverse transformation

technique was then used to obtain variates from an exponential proba-

bility distribution which required the evaluation of a natural logarithm.

Several methods were available to generate random numbers and expo-

nential variates, some of which were more efficient than those used.

The methods used were selected due to their simplicity and immediate

availability.

2. GPSS

GPSS contains eight independent random number generators.

These generators can be synchronized or can operate independently at

the discretion of the programmer.

Two methods are available to generate variates from proba-

bility distributions other than uniform. One method uses the GPSS

FUNCTION statement and a CDF approximated by linear segments. This

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method generates variates by using a random number argument and linear

interpolation on the CDF approximation. This method was used to

generate exponential variates for the torn tape relay model.

The second method uses a GPSS VARIABLE statement to express

the CDF in closed form. Variates can then be generated using the CDF's

inverse transformation function or some other acceptable method. This

method is inconvenient, however, since GPSS contains no internal

routines to evaluate functions such as natural logarithm, sine, gamma,

squareroot, etc. These functions must be evaluated by using GPSS

VARIABLE statements to include the evaluation of power series, etc.

3 . Comparison

GPSS provides adequate methods to generate variates from a

probability distribution in order to represent stocastic phenomena . The

presence of eight random number generators was convenient, but the

lack of GPSS routines to compute common mathematical functions could

prove inconvenient. Stocastic phenomena are easily represented in

FORTRAN and subroutines are available to generate random numbers.

Any number of independent random number generators can be included in

the FORTRAN program. Variates from probability distributions can be

obtained by linear interpolation of the approximated CDF or from the

theoretical distribution in both languages. However, the availability

of FORTRAN library functions often simplifies computing closed form

probability functions compared to the GPSS method.

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D. PROGRAMMING TIME

1. FORTRAN

FORTRAN statements can be written with or without the aid of

a flow chart. A general flow chart containing narrative descriptions of

the actions that are to be portrayed in FORTRAN is often quite useful.

Such a flow chart helps solidify model concepts and often suggests

methods of approach. A detailed statement by statement flow chart is

seldom required except for extremely complicated portions of a program.

The writing of the FORTRAN program for the torn tape relay problem,

after a narrative flow chart had been developed, was comparatively

simple. The FORTRAN program required in excess of 600 statements to

model the system.

2. GPSS

GPSS programming time was considered one of the major

advantages of the language. The GPSS block diagram used to simulate

the system greatly simplified the statement programming of the model.

Once the block diagram had been created, it was a simple matter to

write the program statement associated with each GPSS block. The

GPSS program consisted of 200 statements of which fifty were FUNCTION

and VARIABLE statements and sixty were used to collect statistics for

output purposes.

3 . Comparison

The programming phase of the simulation in GPSS was sig-

nificantly faster than in FORTRAN. Often where one statement was

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needed in GPSS to represent an event, a subroutine was required in FORTRAN

to represent the same event. Consequently, the FORTRAN program required

three times as many statements as needed by GPSS in order to perform

the same task. The time required to program the FORTRAN model was

significantly higher than the three to one ratio indicated by the number

of statements required. It is quite conceivable that a GPSS programmer

could be experimenting with the completed GPSS model while a FORTRAN

programmer was still investigating a method of attack to program the

same system

.

E. COMPUTER RUNNING TIME

1. FORTRAN

The FORTRAN model required seventeen minutes to compile

and execute the same number of runs conducted by the GPSS model in

six minutes. One would generally expect that the FORTRAN program

would execute faster than the GPSS program. This expectation is based

on the fact that FORTRAN is a lower level language and utilizes less

sophisticated data structures and methods to vary the flow of statement

execution. An attempt was made to determine the reason for this lengthy

execution time

.

The probable cause of the excessive time was due to the

method used to advance messages in arrays RR, PP, OO, FF. After a

message was transferred from a terminal station array column, all

message attributes were moved forward one position prior to a new

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message being created. After the message was transferred to a relay

transit bay column, all message arrival times were ordered to insure the

message with the smallest arrival time was in position one of its respectiv

column. The transmission of one routine message required changing

several hundred computer storage values. This perpetual changing of

storage values undoubtedly resulted in a high FORTRAN program execution

time

.

2 . GPSS

The GPSS model of the torn tape relay network required six

minutes and five seconds to execute eight repetitions of the torn tape

networks peak period of operation.

3 . Comparison

Although it may be possible to write faster executing programs

in FORTRAN than in GPSS, the torn tape relay example indicates that

this is not automatic. It appears that the GPSS language includes

efficient routines which when assembled by a programmer into a computer

program provide a comparatively efficient method of building a model.

A GPSS program may not be as efficient as theoretically possible in

FORTRAN. However, for the inexperienced programmer, the efficiency

of the GPSS language may be difficult to match.

The GPSS program written for this study was three times

faster in computer execution time than the FORTRAN program. Twenty-

five replications could have been obtained using the GPSS program as

compared to eight using the FORTRAN program in the same amount of

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computer time. These seventeen additional observations would have sig-

nificantly increased the sample size and provided more confidence in the

results obtained.

F . MONITORING AND DEBUGGING

1. FORTRAN

No set debugging scheme was available to ferret out logic

errors in the FORTRAN program. The syntax diagnostics available are

quite often very hard to correlate with program logic errors. As an

example the FORTRAN program developed several undesired loops that

held simulation time constant while exhausting computer execution

time. The location of these errors was difficult to determine in a single

diagnostic run since the simulation clock time of the errors had to be

determined. This was done by printing the simulation time after each

message was processed. The printout was then used to determine the

simulation time when the undesired loop first occurred. A second diag-

nostic run was then used to obtain information dumps corresponding to

the model simulation time encompassing the undesired loop. A dump

consisted of the simulation time and the relevant arrays. By using

this data, logic errors were isolated by tracing the movement of message

parameters among array columns. This method was quite time consuming

since there existed in excess of 3,000 relevant storage locations. On

several occasions the error could only be isolated to a particular sub-

routine and additional runs and output were required to locate the error.

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Once the location of the undesired loop was located, however, it was a

comparatively simple task to determine the cause and correct the error.

2. GPSS

GPSS debugging and monitoring facilities were excellent.

Chapter 17 of the IBM User's Manual [Ref . 7] provides the programmer

with many valuable hints on monitoring and debugging the GPSS program.

Errors detected during execution of the program triggered an elaborate

information dump which automatically provided the following information:

1. A coded error message

2. Simulation time error was encountered

3 . The block number a transaction was currently in

4. The next block a transaction was to be processed by

5. The number of transactions processed by each block

in the program

6. Current and future event chains

7. GPSS FACILITY statistics

8. QUEUE statistics

9. STORAGE statistics

This dump included ample information to isolate the majority of the

errors encountered debugging the torn tape relay model. However, on

occasion, an additional monitoring and debugging feature was required.

This feature was the GPSS TRACE option. The TRACE feature provided a

capability of tracing a transaction with a given attribute thru the static

structure of the model. Transaction location and parameter values were

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printed as the transaction followed the GPSS block diagram. In addition,

information dumps were easily obtained at strategic locations in the pro-

gram by using a traced transaction to trigger the dump. The dynamics of

the model were then reconstructed using both the information dumps and

the trace block data. From this information, the cause of error was

easily located

.

3 . Comparison

The GPSS automatic information dump that occurred when an

error was detected facilitated the isolation of 90 percent of the errors

encountered. When additional diagnostic information was needed, the

GPSS TRACE option was available. These two features greatly simplified

the task of monitoring the debugging the GPSS torn tape relay network

program. In contrast, the FORTRAN debugging and monitoring error

detection schemes were not suited for detecting logic errors in the simu-

lation model. The method used by the FORTRAN programmer must depend

on the type of error encountered and the particulars of the model. Error

detection required ingenuity, time and often luck in order to locate the

cause of errors in the FORTRAN torn tape relay model.

G. INPUT DATA AND INITIALIZATION

1. FORTRAN

Exogenous data for the torn tape relay was made available

to the model conveniently by use of FORTRAN DATA statements . In

particular it was found by experimentation that the model did not have

to be preloaded with backlogged messages at the beginning of the first

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run. Using DATA statements, the terminal stations and relay transmit

bay stations corresponding to the columns of arrays RR, PP, OO, FF

could have been pre -filled with a desired number of backlogged messages

of any length, destination and arrival time.

2. GPSS

Exogenous data for the GPSS version of the torn tape relay

network was initialized into the model by means of the GPSS FUNCTION.

Although transactions were not preloaded into the GPSS version of the

model to represent a backlogged message condition, preloading could

have been easily accomplished using the GENERATE, and MATRIX blocks.

In GPSS a programmer can specify an upper limit on the number of trans-

actions that will be created by a particular GENERATE block and GENERATE

blocks could have been used to create the desired number of backlogged

messages for each precedence category and station.

3 . Comparison

Exogenous data initialization was handled adequately by

both GPSS and FORTRAN for the torn tape relay network system. Although

the model was not preloaded with backlogged messages for start-up, it

appeared that both GPSS and FORTRAN could have handled the requirement

without difficulty.

Although DATA statements were used for exogenous data in-

put for the FORTRAN model, additional methods were also available,

e.g. , data could also have been inputed by means of magnetic tape or

punched cards. GPSS relies heavily on the FUNCTION statement,

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SAVE VALUE, MATRIX and INITIAL blocks to handle exogenous data require-

ments. GPSS cannot accept magnetic tape input and can only read data

cards with the assistance of the HELP block. However, the IBM manual

[Ref. 7], states that the HELP block is intended only for users who are

thoroughly familiar with the internal operation of the GPSS program. This

last requirement tends to eliminate many hopeful simulators.

GPSS and FORTRAN adequately handled the exogenous data

requirement for the torn tape relay network. However, the FORTRAN

language would be preferable to GPSS if the system to be simulated

required voluminous input data .

H. STORAGE REQUIREMENTS

1. FORTRAN

The FORTRAN model of torn tape relay network required 64K

bytes of computer storage.

2. GPSS

The GPSS model of the torn tape relay network required 12 8K

bytes of computer core storage. GPSS can be operated on the IBM/360/67

in either a 128K or 256K mode. The 256K mode enables a programmer to

utilize an increased number of entities of each category. The 128K

version allocates 150 STORAGE blocks, whereas the 256K version

allocated 300 STORAGE blocks. The only critical factor is the total

amount of storage required by a program. Unused space from one entity

group can be reallocated to another entity group and this allows for an

increase in the number of blocks allocated to a specified entity group.

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An area referred to as GPSS COMMON also requires allocation of storage

space. GPSS COMMON is the space used dynamically for transaction

information, temporary data, and for storing statistical data. The GPSS

torn tape relay network, model required COMMON storage in excess of

that allocated to the 12 8K version. The additional storage for the torn

tape relay model was obtained from unused entity blocks.

3 . Comparison

The FORTRAN model required half the storage required by

the GPSS model, that is 64K versus 128K. This reduced storage require-

ment did not reflect a faster turn around time for the FORTRAN program

due to the long execution time of the program.

I. REPLICATION

1. FORTRAN

Replication for the FORTRAN version of the torn tape relay

network was accomplished by use of a FORTRAN IF statement in con-

junction with the next event clock. Prior to selecting the next event,

a test was conducted to determine if the current simulation time was

in excess of the maximum simulation time for a run (9,000 seconds).

If simulation time was in excess of 9,000 seconds, statement execution

was transferred to record pertinent statistics. After the statistics were

recorded, the number of replications completed was incremented and

tested. If the required number of runs had been completed, the simu-

lation was terminated, if not, the clock was reset and another repli-

cation was performed.

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2. GPSS

Replication is accomplished in GPSS by use of RESET and

CLEAR blocks and by the redefinition of blocks. The RESET block sets

all statistical tables to zero except those specified by the programmer.

The RESET block does not alter the status of any block entities or alter

the values of any transaction parameter values . The CLEAR block per-

forms a function similar to the RESET clock except that in addition all

transactions currently in the system are destroyed.

The GPSS torn tape relay model was replicated with the aid

of RESET blocks and the redefinition of entity blocks in conjunction

with a specially constructed timing program. The timing program was

a simple subprogram that controlled the simulation time for each rep-

lication. The program consisted of a GENERATE block that created a

transaction. This transaction then waited in an ADVANCE block for the

desired time length of each replication (9,000 seconds). The trans-

action was then used to gather and store desired model statistics in

GPSS TABLES. After the statistics were gathered, the transaction was

destroyed. A RESET block then caused entity block statistics to be

zeroed except for specified tables. A START block was then redefined

which caused a new transaction to be created and the above process

was repeated.

3 . Comparison

The GPSS features available to assist the programmer in

replication are very powerful. Specific entity blocks were designed

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to assist the programmer in every facet of replication. Undoubtedly, one

could program the same features into a FORTRAN program, but to do so

would be programmer time consuming and require programmer ingenuity.

J. DATA COLLECTION AND DISPLAY

1. FORTRAN

FORTRAN does not provide any output automatically and all

output desired must be programmed for within the model. This may often

require ingenuity and a considerable amount of programming time. Of

importance ,however , is that desired output can always be obtained in

any format.

2. GPSS

The GPSS program stored statistics in GPSS SAVEVALUES

during the execution of a replication, and the GPSS timing program was

used to collect desired statistics after each replication. The statistics

were stored until the completion of the last replication and then printed

in tabular form .

Some output from GPSS is automatic while other output can

be programmer specified. The automatic output consists of the following:

1 . Block counts

2 . Current value stored in SAVEVALUES

3. USER CHAIN statistics

4. QUEUE statistics

5. FACILITY statistics

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6. STORAGE statistics

7. Relative and absolute clock times

The automatic output is voluminous and provides general information about

the system.

Information relating to transaction,parameters time and specific

facets of the system must be programmer specified. The output can be

obtained either in frequency table or histogram form, the intervals for

which are specified by the programmer. Mean values, standard devia-

tions, maxima, minima and number of observations in each frequency

class are provided as automatic output for table arguments. All attributes

of a modeled system can conceivably be tabulated in a frequency table

or plotted in a histogram. The format of a frequency table cannot be

altered. The programmer can, however, program the dimensions of a

histogram.

3 . Comparison

Data collection and display in FORTRAN is flexible, ob-

trusive and programmer time consuming. In contrast, data collection

in GPSS is non-flexible, unobtrusive and rapidly programmed. FORTRAN

is flexible in that all data can be displayed according to any desired

format. The GPSS format is compact and informative but it cannot be

altered by the programmer.

Data collection and display is obtrusive in FORTRAN because

data collection methods can interfere and obscure the simulation logic

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of the system. GPSS data collection and display statements do not inter-

fere with program logic and can normally be placed in a separate portion

of the program to avoid obscuring the logic of statement execution.

FORTRAN data collection and display techniques require con-

siderable programmer time in engineering the desired display format.

Additionally, all desired output from FORTRAN programs must be pro-

grammed since no output is provided automatically. GPSS automatically

provides a considerable amount of output and allows the programmer to

collect other data at his discretion. The programmer specified output

is rapidly programmed within the simulation since the output format

does not have to be considered.

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V. CONCLUSIONS

The key words in describing the usefulness of FORTRAN for simulation

is flexibility and universal availability. FORTRAN afforded flexibility in

all the areas considered. The analyst may choose the most efficient

methods to reproduce stocastic phenomena. The methods used to represent

the static and dynamic behavior of the system were limited only by the

ingenuity and resourcefulness of the analyst. This flexibility, however,

may be gained at a stiff price. The price paid for flexibility was paid

in man hours spent in conceptualizing the problem, programming, monitor-

ing and debugging the FORTRAN model. For the inexperienced analyst,

flexibility may spell trouble. It is possible for the analyst to select a

comparatively inefficient method, since many diversified methods are

available to model a given system. FORTRAN, regardless of any dis-

advantages, will however still be used extensively for simulation. The

reason being is its universal availability. FORTRAN compilers are

available for nearly all commercially manufactured general purpose

computers

.

The principal advantage of GPSS is that the language is user

oriented. The GPSS language assists the programmer in conceptualizing

the problem, and the GPSS model required reduced programming, debug-

ging and monitoring time compared to the FORTRAN model. The GPSS

block, diagram flow chart closely represented the simulated system, and

the flow chart block mnemonics were quickly convertible to the GPSS

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computer programming language. The above contributed significantly to

reducing the time required to obtain a working simulation model. The

primary disadvantage of GPSS is that output is restricted to bar graphs

and frequency tables. It is conceivable that the GPSS output might have

to be reformated by clerical personnel to conform to specific report require-

ments .

The problem formulation, programming and debugging time that was

saved by GPSS, in contrast to FORTRAN, was of the order of three or

four to one. This time differential is of such magnitude that the analyst

should consider the use of GPSS even if the analyst has had no previous

experience with the language. The advantages of GPSS over FORTRAN

for simulation indicate that GPSS should be used whenever both GPSS

and FORTRAN compilers are available.

It should be noted, however, that GPSS is basically restricted to

the simulation of queueing systems while FORTRAN, as a general purpose

language, can be used to simulate any system that can be described by

a sequence of mathematical expressions.

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APPENDIX A

Exogenous Data

The values utilized for exogenous data were hypothetical but

conceptually realistic. One expects the mean length and arrival rate

of messages to decrease as the precedence of the message increases.

The actual mean values are normally a function of the type of military

units within the geographical area serviced by the terminal. The arrival

rate of messages is normally a function of the time of day. The arrival

rate of messages generally peaks sometime after the end of the normal

work day. Exogenous data that was utilized for both the FORTRAN and

GPSS models is represented in Figures 5 thru 12 of this appendix.

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APPENDIX B

FORTRAN Computer Model

A. Definition of Arrays

1. ARTE (4, 5) contained the mean peak hour arrival rates listed

in Figure ll,Appendix A. Columns corresponded to terminals 1 thru 5 ;

respectively.

2. BACKLP(IO) stored the maximum low precedence backlog of

messages in minutes for each terminal and relay transmitter bay.

3. BACKHP(IO) stored the maximum high precedence backlog of

messages in minutes for each terminal and relay transmitter bay.

4. FF(5,10,3) stored flash message parameters for the terminals

and relay transmit bays. Rows 1 thru 5 stored arrival times, and position

FF (1,1,1) contained the lowest arrival time for terminal one. Columns

1 thru 10 represented terminal stations 1 thru 5, and relay transmitter

bays 6 thru 10, respectively. Relay transmitter bay 6 transmitted messages

to terminal 1, bay 7 transmitted messages to terminal 2, etc. The third

dimension in the array was used to store message attributes as follows:

Position 1 was arrival time, position 2 was message transmission time

and position 3 was destination.

5. HOLDl(i) - HOLD 10 (i) represented the circuits between

terminals and relay transmitter bays. The mnmonics of the HOLD arrays

corresponded to the numbering depicted in Figure 1, Section B, Chapter

III. The dimension of each array was equal to the number of transmit

circuits between two stations and was defined by variables HI thru H10.

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6. NEXEV(20,2) was the array used to store the next event times

for the terminals, relay transmitter bays and groups of transmitter circuits

The transmitter circuits were represented by arrays HOLD1 thru HOLD10.

A message that was transmitted was stored in a HOLD array for the trans-

mission length of the message. Column 1 of array NEXEV recorded the

next event time and column 2 was a statement number corresponding to

the subroutine call statement associated with that event.

7. 00(20,10,3) stored immediate message parameters for the

terminals and relay transmit bays. Rows 1 thru 20 stored arrival times

and position 00(1,1,1) contained the lowest arrival time for terminal

one. Columns 1 thru 10 represented terminal stations 1 thru 5, and

relay transmitter bays 6 thru 10, respectively. Relay transmitter bay 6

transmitted messages to terminal 1, bay 7 transmitted messages to

terminal 2, etc. The third dimension in the array was used to store

message attributes as follows. Position 1 was arrival time, position 2

was message transmission time, and position 3 was destination.

8. PP(30,10,3) stored priority messages for the terminals and

relays. Rows 1 thru 30 stored arrival times and position PP(1,1,1)

contained the lowest arrival time for terminal one. Columns 1 thru 10

represented terminal stations 1 thru 5, and relay transmitter bays 6 thru

10, respectively. Relay transmitter bay 6 transmitted messages to

terminal 1, bay 7 transmitted messages to terminal 2, etc. The third

dimension in the array was used to store message attributes as follows:

Position 1 was arrival time, position 2 was message transmission time,

and position 3 was destination.

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9. 1111(60,10,3) stored routine messages for the terminals and

relays. Rows 1 thru 60 stored arrival times and position RR(1,1,1) con-

tained the lowest arrival time for terminal one. Columns 1 thru 10

represented terminal stations 1 thru 5, and relay transmitter bays 6 thru

10, respectively. Relay transmitter bay 6 transmitted messages to

terminal 1, bay 7 transmitted messages to terminal 2, etc. The third

dimension in the array was used to store message attributes as follows:

Position 1 was arrival time, position 2 was message transmission time,

and position 3 was destination.

10. ZLY(8,5) was initialized to contain the percent peak load

for each station as represented in Figures 5 thru 9, Appendix A.

11. ZLX(8,5) was initialized to contain the time of day cor-

responding to percent peak load for stations 1 thru 5 as represented in

Figures 5 thru 9, Appendix A.

12. ZPTT(5,5) was initialized to contain the percent of messages

transmitted among stations, as depicted by Figure 10, Appendix A.

B. Subroutines

1. BACKLOG (K)

a . Arguments

K was a terminal site number or relay transmitter bay

number, as depicted by Figure 1, Section B, Chapter III.

b. Purpose

Subroutine BACKLOG maintained statistics on the maxi-

mum high and low precedence backlog for each terminal and for each relay

transmitter bay

.

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2. DEST(J,DES)

a. Arguments

J was a value 1,2,3,4 or 5 that represented a terminal

designation. DES was a number 1 thru 5 corresponding to the destination

terminal of the message.

b. Purpose

Subroutine DEST obtained a pseudo-random number and

in conjunction with array ZPTT determined the destination of an originated

message

.

3. FILL(K)

a . Argument

Argument K corresponded to the terminal designators

1,2,3,4 and 5.

b. Purpose

Subroutine FILL created a specified number of messages

of each precedence to initially fill arrays RR, PP , OO and FF . Message

transmission time and destination were also generated for each message.

4. IHOLD(HOLD,L,M)

a . Arguments

HOLD was an array of dimension determined by variables

HI thru H10. The dimension equaled the number of circuits between two

stations. L was the dimension of array HOLD in the subroutine. M was

the row number in array NEXEV(2 0,2) corresponding to the event under

consideration.

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b. Purpose

Subroutine IHOLD was used to release a circuit to

availability after a message was completely transmitted. If two events

had equal next event times, subroutine IHOLD was called prior to sub-

routines TERM or RELAY.

5. INTER (K, TIME, ZNS)

a . Arguments

K was a value 1 thru 5 corresponding to a terminal

designator. TIME was the time of day in seconds. ZNS was the percent

of peak load corresponding to the argument TIME.

b. Purpose

Subroutine INTER performed a linear interpolation on

Figures 1 thru 5 of Appendix A. INTER produced a percent peak load

value for a given time of day.

6. RANDO(IY,YFL)

a. Arguments

LX was in FORTRAN common with the main program and

was initialized an odd integer number. After the initial value had been

specified, LX became a function of IY which also was an integer. YFL

was a pseudo-random number in the range (0,1).

b. Purpose

Subroutine RANDO generated pseudo-random numbers

in the range (0,1).

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7. RELAY(HOLD,K,L,M)

a. Arguments

HOLD was an array of dimension L. L was equal to

the number of transmit circuits. K was the row number in array NEXEV

(20,2) corresponding to the event under consideration.

b. Purpose

RELAY processed messages being transmitted from a

relay transmitter bay to a terminal. The subroutine considered messages

of precedence flash, immediate, priority, and routine on a first in first

out discipline by precedence. Flash messages pre-empted a lower

precedence message if no circuit was available. The message selected

was transferred to the respective HOLD array where it remained for its

transmission time. The backlogged messages at the terminal then

advanced one position in their respective array columns. Necessary

statistics were compiled to determine backlogs and circuit utilization.

The next event time for the given terminal was set in accordance with

circuit availability.

8. RFILL(K,MOVE,PREC)

a . Arguments

K corresponded to the terminal station numbers

1,2,3,4,5 and relay transmitted bay numbers 6,7,8,9,10. If MOVE

equaled 1, RFILL was called by a relay and if 2, RFILL was called by

a terminal

.

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b. Purpose

Subroutine RFILL had two functions. For both the relay

and terminal, the subroutine advanced quequed messages one position

in the message's respective precedence array column. After the messages

had been advanced, at least the last position in the array was vacent.

For a terminal, a new message was generated and was placed in the last

position of the precedence array column.

9. RELREO(K,PREC)

a . Arguments

K referred to relay transmit bay positions, and assumed

values 6,7,8,9 and 10. PREC assumed values of 1,2,3 and 4 that

corresponded to precedences routine, priority, immediate and flash,

respectively.

b. Purpose

Subroutine RELREO ordered message arrival times in

relay transmit bay columns of the precedence arrays. This was done in

order to assure that a message with the lowest arrival time was in

position one for each transmit bay.

10. TERM (HOLD, K,L,M)

a . Arguments

HOLD was an array of dimension L. L was the number

of transmit circuits. K was the row number in array NEXEV (20,2) cor-

responding to the event under consideration.

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b. Purpose

Subroutine TERM processed messages that were trans-

mitted from a terminal to a relay. The subroutine considered messages

of precedence flash, immediate, priority and routine on a first in first

out discipline by precedence. Flash messages pre-empt a lower prece-

dence message if no free circuit was available. A message was trans-

ferred to its respective HOLD array and to a future events list in queue

in the relay transmitter bay that served the desired destination. The

backlogged messages at the terminal advanced one position, and then

a new message was added to the future event list. Necessary statistics

were compiled to determine backlogs and circuit utilization. The next

event time for the given terminal was set in accordance with circuit

availability.

11. UTIL(CLOCK)

a . Arguments

Clock, was a constant equal to the length of computer

run in simulation time units, divided by 1,000.

b. Purpose

UTIL computed the average circuit utilization for each

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Page 78: A GPSS -FORTRAN CASE STUDY by - CORE · H.STORAGEREQUIREMENT FORTRAN GPSS Comparison REPLICATION FORTRAN GPSS Comparison DATACOLLECTIONANDDISPLAY FORTRAN GPSS 3. Comparison V. CONCLUSIONS

FORTRAN FLOW CHART SYMBOLS

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APPENDIX C

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BIBLIOGRAPHY

1. Heidorn, G.E. , A Comparison of SIMSCRIPT and GPSS - HI , un-

published paper, Department of Industrial Administration, Yale

University, August 1966.

2 . Hillier, F.S. , and Lieberman, G.J. , Introduction to Operations

Research , Chapter 14, Holden Day, 1968.

3. International Business Machines, FORTRAN IV Language , Reference

Manual, C28-6515, 8 August 1969.

4. International Business Machines, FORTRAN Programmer's Guide ,

Reference Manual, C28-6630, 29 March 1969.

5. International Business Machines, Messages and Codes OS/SYS/360Operating System , Reference Manual, C28-6631, 5 December 1969.

6. International Business Machines, GPSS User's Manual , Reference

Manual, H20-0326, 26 June 1968.

7. International Business Machines, GPSS Application Description ,

Reference Manual, H20-0186, June 1968.

8. International Business Machines, GPSS Operations Manual ,

Reference Manual, H20-0136, June 1968.

9. Kivat, P.J., Digital Computer Simulation: Computer Programming

Languages , Memorandum RM-5883-PR, The Rand Corporation,

January 1969

.

10. Kivat, P.J., Digital Computer Simulation: Modeling Concepts ,

Memorandum RM-5378-PR, The Rand Corporation, August 1967.

11 . Kivat, P.J. , and Fishman, G.S. , Digital Computer Simulation :

Statistical Considerations , Memorandum RM-5387-PR, November 1967,

12 . Naylor, T .H . , and others , Computer Simulation Technigues ,

Wiley, April 1968.

13. Merikallio, A.E., The Past, Present and Future in GeneralSimulation Languages , Management Science, v. 6, p. 236-267,November 1964 .

146

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14. Schriber, T.J., General Purpose Simulation System/3 60, Introductory-

Concepts and Case Studies , University of Michigan Press, Pre-

liminary Edition, September 1968.

15 . Tiechroew, D. , and Lubin, F .J. , Computer Simulation-Discussion of

the Technique and Comparison of Languages , Communications of the

ACM, v. 9, p. 723-741, October 1966.

16 . Tiechroew, D. , Lubin, F . J . , and Truit, T . D . , Discussion of

Computer Simulation Techniques and Comparison of Languages ,

Simulation, v. 9, p. 95-98, August 1967.

17. Tocher, K.D., Review of Simulation Languages , Operational ResearchQuarterly, v. 16, p. 189-218, June 1965.

18. Weinert, A.E., A SIMSCRIPT-FORTRAN Cast Study , Communicationsof the ACM, v. 10, p. 784-793, December 1967.

147

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INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 20

Cameron Station

Alexandria, Virginia 22314

2. Library, Code 0212 2

Naval Postgraduate SchoolMonterey, California 93 940

3. Department of Operations Analysis (Code 55) 2

Naval Postgraduate School

Monterey, California 93 940

4. Assoc. Professor Alvin F . Andrus 1

Department of Operations Analysis

Naval Postgraduate SchoolMonterey, California 93940

5. Civil Schools Branch 1

Office of Personnel Operations

Washington, D. C. 20315

6. Major Charles J. Petronis 1

159 Ashford Ave.Dobbs Ferry, New York 10522

INTERNALLY DISTRIBUTED

REPORT

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Security Classification

DOCUMENT CONTROL DATA -R&D(Security clas si lie at ion ol title, body ol abstract and indexing annotation must be entered when the overall report is classified)

originating activity (Corporate author)

Naval Postgraduate School

Monterey, California 93940

2a. REPORT SECURITY CLASSIFICATION

Unclassified26. GROUP

REPORT TITLE

A GPSS-FORTRAN Case Study

DESCRIPTIVE NOTES (Type ol report and, inclusive dates)

Master's Thesis; April 1970au THORIS) (First name, middle initial, last name)

Charles Joseph Petronis

REPOR T D A TE

April 1970

7a. TOTAL NO. OF PAGES

149

76. NO. OF REFS

18I. CONTRACT OR GRANT NO.

b. PROJEC T NO

9a. ORIGINATOR'S REPORT NUMBER(S)

06. OTHER REPORT NOISI (Any other numbers that may be assignedthis report)

DISTRIBUTION STATEMENT

This document has been approved for public release and sale; its distribution

is unlimitedI. SUPPLEMENTARY NOTES 12. SPONSORING MILI TAR Y ACTIVITY

Naval Postgraduate School

Monterey, California 93 940

I. ABSTRACT

The objective of this study was to compare two commonly used computer simulation

languages: GPSS and FORTRAN. The comparison was made by simulating an

identical system in both languages. The comparison criteria used to evaluate the

languages were as follows: ability to represent system, simulation time, ability

to represent stocastic phenomena, programming time, computer running time,

monitoring and debugging, storage requirements, data initialization and starting

conditions, replication, data collection and display. The results from this study

indicated that a system may be modeled four to five times faster using GPSS as

compared to FORTRAN. The modeled system was simpler to conceptualize in GPSS,and the model required reduced programming, debugging and monitoring time com-pared to the FORTRAN model.

>D ."i" .1473'N 01 01 -807-681 1

(PAGE 1) 149

Security ClassificationA- 3 1408

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Security Classification

key wo R D s

GPSSFORTRANComputer simulation

Computer language

Computer language comparison

DD ,T:..1473 back) 150

'I

• 9 7 • e S 2 1 Security Classification A - 3 t 409

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Thesis 120927P457 Petronisc.l A GPSS-FORTRAN

case study.

1 '"• ^ Q 9 7Thesis 161)36^P457 PetronisCK1 A GPSS-FORTRAN

case study.

L

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thesP457

A GPSS-FORTRAN case study.

3 2768 001 00185 2DUDLEY KNOX LIBRARY