CONTENTS
Preface = xiii
Chapter I Basic Simulation Modeling = 1
1.1 The Nature of Simulation = 1
1.2 Systems, Models, and Simulation = 2
1.3 Discrete-Event Simulation = 4
1.3.1 Time-Advance Mechanisms = 4
1.3.2 Components and Organization of a Discrete-Event Simulation Model = 6
1.3.3 Advantages and Disadvantages of Simulation = 8
1.4 Simulation of a Single-Server Queueing System = 9
1.4.1 Statement of the Problem = 9
1.4.2 Intuitive Explanation = 11
1.4.3 FORTRAN Program = 15
1.4.4 Simulation Output and Discussion = 25
1.4.5 Alternative Stopping Rules = 27
1.5 Simulation of an Inventory System = 28
1.5.1 Statement of the Problem = 28
1.5.2 FORTRAN Program = 32
1.5.3 Simulation Output and Discussion = 42
1.6 Steps in a Discrete-Event Simulation Study = 43
1.7 Other Types of Simulation = 46
1.7.1 Continuous Simulation = 46
1.7.2 Combined Discrete-Continuous Simulation = 47
1.7.3 Monte Carlo Simulation = 49
Appendix IA: Fixed-Increment Time Advance = 50
Appendix I B: A Primer on Queueing Systems = 51
IB.1 ComponentsofaQueueingSystem = 52
IB.2 Notation for Queueing Systems = 53
IB.3 Measures of Performance for Queueing Systems = 54
Problems = 55
References = 57
Chapter 2 Modeling Complex Systems = 59
2.1 Introduction = 59
2.1.1 Approaches to Storing Lists in a Computer = 60
2.2 Linked Storage Allocation = 60
2.3 A Simple Simulation Language, SIMLIB = 65
2.4 A Time-Shared Computer Model = 70
2.4.1 Statement of the Problem = 70
2.4.2 SIMLIB Program = 71
2.4.3 Simulation Output and Discussion = 79
2.5 A Multiteller Bank with Jockeying = 79
2.5.1 Statement of the Problem = 79
2.5.2 SIMLIB Program = 80
2.5.3 Simulation Output and Discussion = 85
2.6 A Job-Shop Model = 85
2.6.1 Statement of the Problem = 85
2.6.2 SIMLIB Program = 90
2.6.3 Simulation Output and Discussion = 99
2.7 Efficient EvOnt-List Manipulation = 100
Appendix 2A: FORTRAN Listings for SIMLIB = 101
Problems = 102
References = 113
Chapter 3 Simulation Languages = 114
3.1 Introduction = 114
3.2 Comparison of Simulation Languages with General-Purpose Languages = 115
3.3 Approaches to Discrete-Event Simulation Modeling = 116
3.4 GASP IV and Related I-anguages = 118
3.4.1 Simulation of the M／M／I Queue = 119
3.4.2 SLAM = 123
3.5 SIMSCRIPT Ⅱ.5 = 124
3.5.1 Simulation of the M／M／ⅠQueue = 125
3.5.2 The Process-Interaction Approach in SIMSCRIPT Ⅱ.5 = 128
3.6 GPSS = 129
3.6.1 Simulation of the M／M／ⅠQueue = 130
3.7 Criteria for Selecting a Simulation Language = 133
Problems = 135
References = 136
Chapter 4 Review of Basic Probability and Statistics = 137
4.1 Introduction = 137
4.2 Random Variables and Their Properties = 137
4.3 Simulation Output Data and Stochastic Processes = 142
4.4 Estimation of Means, Variances, and Correlations = 145
4.5 Confidence Intervals and Hypothesis Tests for the Mean = 148
4.6 The Strong Law of Large Numbers = 151
Appendix 4A: Comments on Covariance Stationary Processes = 152
Problems = 153
References = 154
Chapter 5 Selecting Input Probability Distributions = 155
5.1 Introduction = 155
5.2 Useful Probability Distributions = 157
5.2.1 Parameterization of Distributions = 157
5.2.2 Continuous Distributions = 158
5.2.3 Discrete Distributions = 170
5.2.4 Empirical Distributions = 176
5-3 Hypothesizing a Family of Distributions = 177
5.3.1 Continuous Distributions = 178
5.3.2 Discrete Distributions = 187
5.4 Estimation of Parameters = 188
5.5 Goodness-of-Fit Tests = 192
5.5-1 Informal Visual Assessment = 193
5.5.2 Chi-Square Test = 194
5.5.3 KolmogoEOV-Smirnov Tests = 199
5.5.4 POissOn Process Test = 203
5.5.5 Other Tests = 204
5.6 Selecting a Distribution in the Absence of Data = 204
5.7 Models of Arrival Processes = 206
5.7.1 POisson Process = 206
5.7.2 Nonstationary Poisson Process = 207
5.7.3 Batch Arrivals = 209
Appendix 5A: Shifted and Truncated Distributions = 210
Appendix 5B: Tables of MLEs for the Gamma and Beta Distributions = 212
Problems = 214
References = 216
Chapter 6 Random-Number Generators = 219
6.1 Introduction = 219
6.2 Linear Congruential Generators = 222
6.2.1 Mixed Generators = 224
6.2.2 Multiplicative GENERATORS = 225
6.3 Other Kinds of Generators = 228
6.3.1 More General Congruences = 228
6.3.2 Composite Generators = 229
6.3-3 TauswortHe Generators = 230
6.4 Testing Random-Number Generators = 231
6.4.1 Empirical Test = 231
6.4.2 Theoretical Tests = 235
6.4.3 Some General Observations on Testing = 236
Problems = 236
References = 238
Chapter 7 Generating Random Variables = 240
7.1 Introduction = 240
7.2 General Approaches to Generating Random Variables = 242
7.2.1 Inverse Transform = 242
7.2.2 Composition = 247
7.2.3 Convolution = 249
7.2.4 Acceptance-Rejection = 250
7.2.5 Special Properties = 252
7.3 Generating Continuous Random Variables = 253
7.3.1 Uniform = 253
7.3.2 Exponential = 254
7.3.3 m-Eriang = 254
7.3.4 Gamma = 255
7.3.5 Weibull = 260
7.3.6 Normal = 260
7.3.7 Lognormal = 259
7.3.8 Beta = 260
7.3.9 Triangular = 261
7.3.10 Empirical Distributions = 261
7.4 Generating Discrete Random Variables = 262
7.4.1 Bernoulli = 263
7.4.2 Discrete Uniform = 263
7.4.3 Arbitrary Discrete Distribution = 263
7.4.4 Binomial = 266
7.4.5 Geometric = 266
7.4.6 Negative Binomial = 266
7.4.7 Poisson = 267
7.5 Generating Correlated Random Variables = 267
7.5.1 Using Conditional Distributions = 268
7.5.2 Multivariate Normal and Multivariate Lognormal = 269
7.5.3 Correlated Gamma Random Variables = 269
7.6 Generating Arrival Processes = 270
7.6.1 Poisson Process = 270
7.6.2 Nonstationary Poisson Process = 271
7.6.3 Batch Arrivals = 272
Appendix 7A: Validity of the Acceptance-Rejection Method = 273
Problems = 274
References = 277
Chapter 8 Output Data Analysis for a Single System = 279
8.1 Introduction = 279
8.2 Types of Simulations with Regard to Analysis of the Output = 280
8.3 Measures of System Performance = 282
8.3.1 Contrast of Measures of Performance = 282
8.3.2 The Meaning of Steady State
8.3.3 Measures of Performance Other than Averages = 285
8.4 The Need for Confidence Intervals = 287
8.5 Confidence Intervals for Terminating Simulations = 287
8.5.1 Fixed-Sample-Size Procedure = 288
8.5.2 Obtaining Confidence Intervals with a Specified Precision = 291
8.5.3 Recommended Use of the Procedures = 293
8.5.4 Approaches to Choosing Appropriate Initial Conditions = 294
8.6 Confidence Intervals for Steady-State Simulations = 295
8.6.1 Fixed-Sample-Size Procedures = 295
8.6.2 Sequential Procedures = 302
8.6.3 A Replication-Deletion Approach = 307
8.7 Multiple Measures of Performance = 308
8.8 Concluding Thoughts on the Chapter = 310
Appendix 8A: The Memoryless Property = 311
Appendix 8B: Ratios of Expectations and Jackknife Estimators = 311
Problems = 313
References = 314
Chapter 9 Statistical Techniques for Comparing Alternative Systems = 316
9.1 Introduction = 316
9.2 Confidence Intervals for the Difference between Measures of Performance of Two Systems = 319
9.3 Selecting the Best of k Systems = 322
9.4 Selecting a Subset of Size m Containing the Best of k Systems = 325
9.5 Selecting the m Best of k Systems = 326
9.6 Validity of the Selection Procedures = 327
Appendix 9A: Constants for the Selection Procedures = 329
Problems = 331
References = 331
Chapter 10 Validation of Simulation Models = 333
10.1 Introduction = 333
10.2 Verification of Simulation Models = 334
10.3 General Perspectives on Validation = 337
10.4 A Three-Step Approach to Validation = 338
10.4.1 Develop a Model with High Face Validity = 338
10.4.2 Test the Assumptions of the Model Empirically = 339
10.4.3 Determine How Representative the Simulation Output Data Are = 340
10.5 Additional Considerations in Validation = 342
10.6 Statistical Procedures for Comparing Real-World Observations and Simulation Output Data = 343
10.6.1 An Inspection Approach = 343
10.6.2 A Confidence-Interval Approach = 345
10.6.3 Time-Series Approaches = 347
Problems = 347
References = 348
Chapter 11 Variance-Reduction Techniques = 349
11.1 Introduction = 349
11.2 Common Random Numbers = 350
11.3 Antithetic Variates = 354
11.4 Control Variates = 357
11.5 Indirect Estimation = 361
11.6 Conditional Expectations = 363
Problems = 366
References = 368
Chapter 12 Experimental Design and Optimization = 370
12.1 Introduction = 370
12.2 2 2k Factorial Designs = 372
12.3 2 2k -P Fractional Factorial Designs = 376
12.4 Response-Surface Methodology = 379
Problems = 381
References = 382
Appendix = 385
Index = 389
