CONTENTS
1 SYSTEM MODELS
1-1 The Concepts of a System = 1
1-2 System Environment = 3
1-3 Continuous and Discrete Systems = 4
1-4 System Modeling = 5
1-5 Types of Models = 7
1-6 Physical Models = 8
1-7 Mathematical Models = 10
1-8 Principles Used in Modeling = 12
2 SYSTEM SIMULATION
2-1 Definition of System Simulation = 17
2-2 Experimental Nature of Simulation = 18
2-3 Steps Involved in Simulation Studies = 21
2-4 Recurrence Models = 22
2-5 Cobweb Models = 24
2-6 Simulation Programming Languages = 25
2-7 System Simulation Applications = 26
3 COHTINOUOS SYSTEM SIMUALTION
3-1 Continuous System Models = 29
3-2 Linear Differential Equations = 30
3-3 Analog Computers = 31
3-4 Digital-Analog Simulators = 33
3-5 The 1130 Continuous System Modeling Prograln(CSMP) = 33
3-6 Digital-Analog Solution of Linear Differential Equations = 35
3-7 Simultaneous Equations = 38
3-8 Continuous System Simulation Languages = 38
3-9 360/CAMP = 39
3-10 360/CSMP Examples = 42
4 INDUSTRIAL DYNAMICS
4-1 Concepts of Industrial Dynamics = 49
4-2 Industrial Dynanlics Diagrams = 50
4-3 A Simple Industrial Dynamics Model = 51
4-4 Representation of Delays = 53
4-5 Feedback Systems = 55
4-6 Feedback in Industrial Systems = 58
4-7 Inventory Control Systems = 59
4-8 Industrial Dynamics Model of an Inventory Control System = 60
4-9 Further Development of the Inventory Control System Model = 63
5 THE DYNAMO PROGRAMMING LANGUAGE
5-1 DYNAMO = 69
5-2 Representation of Time = 69
5-3 Choice of Solution Interval = 70
5-4 Equation Forms = 71
5-5 Delays = 73
5-6 Durable Goods Industry Model = 74
5-7 Customer Sector = 76
5-8 Retail Sector = 76
5-9 Other Sectors = 78
5-10 Initial Conditions = 79
5-11 Coding of the Problem = 80
5-12 DYNAMO Output = 80
6 PROBABILITY CONCEPTS IN SIMULATION
6-1 Stochastic Variables = 85
6-2 Probability Functions = 86
6-3 Numerical Derivation of Continuous Probability Functions = 88
6-4 Monte Carlo Simulation = 90
6-5 Continuous Uniformly Distributed Random Numbers = 92
6-6 Computer Generation of Random Numbers = 93
6-7 A Uniform Random Number Generator = 96
6-8 Generating Discrete Distributions = 97
6-9 Non-Uniform Continuous Random Number Generators = 98
7 ARRIVAL PATTERNS AND SERVICE TIMES
7-1 Congestion in Systems = 105
7-2 Arrival Patters = 106
7-3 Poisson Arrival Patterns = 107
7-4 The Exponential Distribution = 108
7-5 The Coefficient of Variation = 110
7-6 The Erlang Distribution = 111
7-7 The Hyper-Exponential Distribution = 112
7-8 Service Times = 113
7-9 The Normal Distribution = 114
7-10 Queuing Disciplines = 117
7-11 Measures of Queues = 118
7-12 Mathematical Solutions of Queuing Problems = 119
8 DISCRETE SYSTEM SIMULATI0N
8-1 Discrete Events = 123
8-2 Representation orTime 124
8-3 Generation of Arrival Patterns = 124
8-4 Simulation of a Telephone System = 125
8-5 Simulation Programming Tasks = 130
8-6 A Simulation Program Flow Chart = 132
8-7 Discrete Simulation Languages = 134
9 SIMULATION WITH FORTRAN
9-1 The use of FORTRAN for Simulation = 141
9-2 A FORTAN Simulation of the Telephone System = 142
9-3 Organization of the Program = 143
9-4 Construction of the System Image = 144
9-5 Random Number Subroutine = 145
9-6 Program Initialization = 147
9-7 Finding the Next Potential Event = 149
9-8 Testing of a Call Can be Connected = 152
9-9 Connecting a Call = 153
9-10 Desconnecting a Call = 154
9-11 Gathering Statistics = 154
9-12 Output Report = 156
10 SIMULATION PROGRAMMING TECHNIQUES
10-1 Gathering Statistics = 163
10-2 Counters and Summary Statistics = 164
10-3 Measuring Utilization and Occupancy = 165
10-4 Recording Distributions = 166
10-5 FORTRAN Programs for Statistics = 167
10-6 List Structures = 170
10-7 Extension of the Telephone System Example = 176
10-8 Simultaneous Events = 183
10-9 Blocked Events = 185
11 INTRODUCTION TO GPSS
11-1 General Description = 191
11-2 Action Times = 195
11-3 Succession of Events = 196
11-4 Choice of Paths = 196
11-5 Simulation of a Manufacturing Shop = 197
11-6 Facilities and Storages = 201
11-7 Gathering Statistics = 204
11-8 Conditional Transfers = 206
11-9 Program Control Cards = 209
12 GPSS EXAMPLES
12-1 Priorities and Parameters = 215
12-2 Standard Numerical Attributes = 216
12-3 functions = 218
12-4 Transfer Modes = 220
12-5 Simulation of a Supermarket = 221
12-6 Logic Switches = 225
12-7 Testing Conditions = 226
12-8 Indirect Addressing = 227
12-9 GPSS Model of a Simple Telephone System = 229
12-10 Set Operations = 232
13 INTRODUCTION TO SIMSCRIPT
13-1 SIMSCRIPT Programs = 239
13-2 SIMSCRlPT System Concepts = 240
13-3 The Definition Form = 241
13-4 Referencing Variables = 244
13-5 Organization of a SIMSCRIPT Program = 245
13-6 Event Notices = 247
13-7 Programming Event Routines = 248
13-8 Management of Temporary Entities and Event Notices = 249
13-9 SIMSCRIPT Commands = 251
13-10 The Telephone System in SIMSCRIPT = 253
13-11 Report Generation = 256
13-12 Initialization = 258
13-13 Control Cards = 260
14 MANAGERMENT OF SETS IN SIMSCRIPT
14-1 Definition of Sets in SIMSCRIPT = 263
14-2 Telephone System, Model 2 = 264
14-3 Searching Sets = 268
14-4 Searching Arrays = 272
14-5 DO Loops = 273
14-6 Statistical Commands = 274
15 VERIFICATION OF SIMULATION RESULTS
15-1 Nature of the Problem = 277
15-2 Estimation Methods = 278
15-3 Simulation Run Statistics = 279
15-4 Repetition of Runs = 282
15-5 Elimination of Initial Bias = 284
15-6 Batch Means = 289
15-7 Time Serries Analysis = 290
15-8 Spectral Analysis = 291
Index = 295
