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Tables of Contents for Modern Statistical, Systems, and Gpss Simulation
Chapter/Section Title
Page #
Page Count
Preface to the First Edition
v
4
Preface to the Second Edition
ix
4
About the Authors
xiii
1 Discrete Event Computer Simulation
1
58
1.1 Computer Implementation of Simulations
4
2
1.2 The Single-Server Queue
6
13
1.2.1 A Single-Server Queueing Model
7
2
1.2.2 An Improved Model for the Single-Server Queue
9
5
1.2.3 Generation of Arrival Times and Other Attributes
14
5
1.3 The Single-Server Queue: Additional Goals
19
3
1.4 GPSS Model of the Single-Server Queue
22
4
1.5 Single-Server Queue with Priority Classes: Data Structures
26
9
1.5.1 Use of Ranked List Structures
26
1
1.5.2 Use of Floating File Structures
27
2
1.5.3 Linked-List Priority Queues
29
1
1.5.4 Double-Pointing Structures
30
5
1.6 Theoretical Results about the Single-Server Queue
35
11
1.6.1 Poisson Arrivals and Exponential Interarrival Times
36
2
1.6.2 Number of Customers in M/M/1/XXX Queueing Systems
38
3
1.6.3 Idle Time in M/M/1/XXX Queues
41
1
1.6.4 Expected Number of Customers in M/M/1/XXX Queues
41
1
1.6.5 Expected Number of Customers in the Facility and in the Queue of an M/M/1/XXX System
42
1
1.6.6 Expected Time Spent Waiting and in the System
42
2
1.6.7 Summary of Results and an Example
44
2
1.7 Use of Efficient Sorting Techniques in Simulation
46
4
Problems for Chapter 1
50
9
2 Introduction to GPSS
59
30
2.1 GPSS Program Structure
59
2
2.2 The SIMULATE, START, and END Statements
61
1
2.3 The GENERATE and TERMINATE Blocks
62
3
2.4 Facilities and the SEIZE and RELEASE Blocks
65
1
2.5 The ADVANCE Block
66
1
2.6 Queues and the QUEUE and DEPART Blocks
67
1
2.7 GPSS Program Output
68
3
2.8 Storages and the ENTER and LEAVE Blocks
71
3
2.9 The TRANSFER Block
74
3
2.10 Example: An Appliance Repair Shop
77
7
Problems for Chapter 2
84
5
3 Random Number Generation and Testing
89
62
3.1 History and Variety of Random Number Generation Methods
91
6
3.2 Traditional Quality Measures of Random Number Generators
97
5
3.3 Statistical Quality Measures of Random Number Generators
102
13
3.3.1 Uniformity of Distribution Test
104
1
3.3.2 Coupon Collector's Test
105
1
3.3.3 Gap Test
106
1
3.3.4 Permutation Test
106
1
3.3.5 Poker Test
106
3
3.3.6 Runs-Up Test
109
2
3.3.7 Serial Pairs Test
111
1
3.3.8 Chi-Square on Chi-Squares Test (CSCS Test)
111
2
3.3.9 Entropy-Uniformity Test
113
2
3.4 Theoretical Tests of Random Number Generators
115
7
3.4.1 Serial Correlation Test
115
1
3.4.2 Interplanar Distance (or Spectral) Test
116
6
3.5 Test Results on Specific Random Number Generators
122
21
3.5.1 Random Number Generators
123
10
3.5.2 Tests of Random Number Generators and Their Results
133
10
3.6 Notes on the Use of TESTRAND
143
3
Problems for Chapter 3
146
5
4 Random Variable Generation
151
94
4.1 Selection of a Distribution
152
2
4.2 Generating Univariate Random Variables: Inverse Distribution Function Method
154
9
4.2.1 The Exponential Distribution
157
1
4.2.2 The Bernoulli Distribution
158
1
4.2.3 The Normal Distribution
159
2
4.2.4 The Uniform Distribution
161
1
4.2.5 The Binomial Distribution
161
2
4.3 Generating Univariate Random Variables: Discrete Distributions
163
5
4.4 Generating Poisson and Geometric Random Variables (Discrete Univariate Distributions that Take on Infinitely Many Values)
168
5
4.4.1 The Poisson Distribution
168
2
4.4.2 The Geometric Distribution
170
3
4.5 Generating Bivariate and Multivariate Discrete Distributions
173
2
4.6 Generating Specific Univariate Distributions
175
20
4.6.1 The Binomial Distribution
175
3
4.6.2 The Normal Distribution
178
7
4.6.3 The Chi-Square Distribution
185
1
4.6.4 Student's t-Distribution
186
4
4.6.5 The Erlang Distribution
190
1
4.6.6 Double-Exponential Distribution: Via Exponential
191
1
4.6.7 The F Distribution: Via Chi-Squares
192
1
4.6.8 The Beta Distribution
192
2
4.6.9 The Weibull Distribution: Via the Exponential
194
1
4.6.10 The Lognormal Distribution: Via the Normal
194
1
4.6.11 The Gamma Distribution
194
1
4.7 Generating p.d.f.s. Bounded on a Closed Interval
195
5
4.8 Generating Multivariate Normal Random Variables
200
4
4.9 Confidence Regions for Multivariate Normal Random Variables
204
4
4.10 Fitting Distributions to Data: The GLD Family, Univariate and Bivariate
208
20
4.10.1 The Parameter Space of the GLD
211
5
4.10.2 Estimation of the GLD Parameters
216
4
4.10.3 The Extended GLD
220
4
4.10.4 Bivariate GLD Distribution: The GLD-2
224
4
4.11 Empiric Distribution Function and Empiric p.d.f.
228
5
4.12 Sampling from a Histogram
233
4
4.13 Fitting a Normal (Univariate or Multivariate) Distribution
237
4
Problems for Chapter 4
241
4
5 Intermediate GPSS
245
50
5.1 Transaction Movement
245
7
5.2 The START Statement and Chain Output
252
4
5.3 Random Number Generators Built into GPSS
256
1
5.4 The RESET, RMULT, and CLEAR Control Statements
256
5
5.5 GPSS Functions
261
8
5.5.1 Discrete Functions
262
3
5.5.2 Continuous Functions
265
4
5.6 Example: A Manufacturing Shop
269
8
5.7 Sampling: The Exponential Distribution
277
2
5.8 Arithmetic Variables in GPSS
279
2
5.9 Sampling: The Normal Distribution
281
1
5.10 Transaction Parameters and the ASSIGN Block
281
2
5.11 Example: A Batch Computer System Operation
283
6
Problems for Chapter 5
289
6
6 Statistical Design and Analysis of Simulations
295
34
6.1 How Long to Simulate: Goal of Estimating the Mean
295
10
6.1.1 The Proportional Closeness Goal
300
2
6.1.2 Case Study of Estimating Demand for Emergency Services
302
3
6.2 How Long to Simulate: Estimating the Difference Mu(1) - Mu(2)
305
1
6.3 How Long to Simulate: Goal of Selection of the Best
306
6
6.4 System Optimization via Statistical Design and Regression
312
7
6.4.1 Example: A Time-Shared Computer System
313
3
6.4.2 Central Composite Design for Kappa = 2 Variables
316
3
6.5 Statistical Simulation and the "Bootstrap" Method
319
1
6.6 The Generalized Bootstrap
320
2
6.7 Other Statistical Design and Analysis Aspects of Simulation
322
3
6.7.1 Estimation of a Percentile Point
323
1
6.7.2 Estimation of Var(X)
324
1
6.7.3 Variance Reduction Techniques
324
1
Problems for Chapter 6
325
4
7 Advanced GPSS Features
329
72
7.1 Standard Numerical Attributes
329
6
7.1.1 Facilities
331
2
7.1.2 Queues
333
1
7.1.3 Storages
333
1
7.1.4 Blocks
334
1
7.1.5 Transactions
334
1
7.1.6 The Clock
334
1
7.1.7 Other SNAs
335
1
7.2 Savevalues, the INITIAL Statement, and the SAVEVALUE Block
335
4
7.2.1 The INITIAL Statement
335
2
7.2.2 The SAVEVALUE Block
337
2
7.3 Example: A Repair Service Operation
339
4
7.4 The PRINT Block
343
3
7.5 Example: Demand Estimation
346
2
7.6 User-Defined Random Number Generators
348
3
7.7 Transit Time and the MARK Block
351
3
7.8 The TABLE Statement and the TABULATE Block
354
5
7.8.1 The TABLE Statement
354
1
7.8.2 The TABULATE Block
355
2
7.8.3 Variations of the TABLE Statement
357
2
7.9 The PRIORITY, PREEMPT, and RETURN Blocks
359
5
7.9.1 The PRIORITY Block
359
1
7.9.2 The PREEMPT and RETURN Blocks
360
1
7.9.3 Preempted Transactions
361
3
7.10 Example: Emergency Medical System
364
5
7.11 SNA Comparisons and the TEST Block
369
4
7.12 Example: A Time-Shared Computer System
373
4
7.13 The LOOP Block
377
2
7.14 Logic Switches, INITIAL Statements, LOGIC and GATE Blocks
379
5
7.14.1 Initialization of Logic Switches
379
1
7.14.2 The LOGIC Block
380
1
7.14.3 Logic Switches and the GATE Block
380
1
7.14.4 Other Forms of the GATE block
381
3
7.15 The SELECT Block
384
3
7.15.1 The Relational Mode
384
2
7.15.2 The Min-Max Mode
386
1
7.15.3 The Logical Mode
386
1
7.16 Example: A Multiple-Checkout Supermarket Operation
387
5
7.17 User Chains and the LINK and UNLINK Blocks
392
3
Problems for Chapter 7
395
6
8 Case Study of a Simulation: Design, Analysis, Programming
401
46
8.1 Description of the Transportation System Problem
401
4
8.2 Statistical Design
405
4
8.2.1 Statistically Designed Experimentation
405
1
8.2.2 Naive Experimentation
406
3
8.3 Statistical Analysis
409
25
8.3.1 Analysis of Data
409
4
8.3.2 Statistical Programming in SAS for Data Analysis
413
21
8.4 The GPSS Program
434
10
8.4.1 Functions, Variables, and Savevalues
434
1
8.4.2 The Program Logic
435
2
8.4.3 Program Output
437
7
Problems for Chapter 8
444
3
Appendices
447
54
A Using GPSS/PC
447
12
A.1 Running a GPSS/PC Program
448
1
A.2 Interacting with GPSS/PC
449
1
A.3 GPSS/PC Output
450
1
A.4 The GPSS/PC Models on the Disk
450
1
A.5 Debugging in GPSS/PC
451
8
B GPSS Block Statement Formats
459
10
C The Normal Distribution
469
4
D The Student's t-Distribution
473
2
E The Chi-Square Distribution
475
4
F The Chi-Square Distribution with 99 Degrees of Freedom
479
2
G Random Numbers
481
14
H Tables for Selection of the Best
495
6
References and Author Index
501
12
Subject Index
513