Modern Statistical, Systems, and GPSS Simulation, Second Edition

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ISBN: 9780849339226 | 0849339227
Cover: Hardcover
Copyright: 11/9/1998

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Modern Statistical, Systems, and GPSS Simulation, Second Edition introduces the theory and implementation of discrete-event simulation. This text:o establishes a theoretical basis for simulation methodologyo provides details of an important simulation language (GPSS - General Purpose Simulation System)o integrates these two elements in a systems simulation case studyValuable additions to the second edition include coverage of random number generators with astronomic period, new entropy-based tests of uniformity, gamma variate generation, results on the GLD, and variance reduction techniques.GPSS/PC is an interactive implementation of GPSS for the IBM-PC compatible family of microcomputers. The disk accompanying Modern Statistical, Systems, and GPSS Simulation contains the limited educational version of GPSS/PC with many illustrative examples discussed in the text.

Preface to the First Edition

(4)

Preface to the Second Edition

(4)

About the Authors

xiii

1 Discrete Event Computer Simulation

(58)

1.1 Computer Implementation of Simulations

(2)

1.2 The Single-Server Queue

(13)

1.2.1 A Single-Server Queueing Model

(2)

1.2.2 An Improved Model for the Single-Server Queue

(5)

1.2.3 Generation of Arrival Times and Other Attributes

(5)

1.3 The Single-Server Queue: Additional Goals

(3)

1.4 GPSS Model of the Single-Server Queue

(4)

1.5 Single-Server Queue with Priority Classes: Data Structures

(9)

1.5.1 Use of Ranked List Structures

(1)

1.5.2 Use of Floating File Structures

(2)

1.5.3 Linked-List Priority Queues

(1)

1.5.4 Double-Pointing Structures

(5)

1.6 Theoretical Results about the Single-Server Queue

(11)

1.6.1 Poisson Arrivals and Exponential Interarrival Times

(2)

1.6.2 Number of Customers in M/M/1/XXX Queueing Systems

(3)

1.6.3 Idle Time in M/M/1/XXX Queues

(1)

1.6.4 Expected Number of Customers in M/M/1/XXX Queues

(1)

1.6.5 Expected Number of Customers in the Facility and in the Queue of an M/M/1/XXX System

(1)

1.6.6 Expected Time Spent Waiting and in the System

(2)

1.6.7 Summary of Results and an Example

(2)

1.7 Use of Efficient Sorting Techniques in Simulation

(4)

Problems for Chapter 1

(9)

2 Introduction to GPSS

(30)

2.1 GPSS Program Structure

(2)

2.2 The SIMULATE, START, and END Statements

(1)

2.3 The GENERATE and TERMINATE Blocks

(3)

2.4 Facilities and the SEIZE and RELEASE Blocks

(1)

2.5 The ADVANCE Block

(1)

2.6 Queues and the QUEUE and DEPART Blocks

(1)

2.7 GPSS Program Output

(3)

2.8 Storages and the ENTER and LEAVE Blocks

(3)

2.9 The TRANSFER Block

(3)

2.10 Example: An Appliance Repair Shop

(7)

Problems for Chapter 2

(5)

3 Random Number Generation and Testing

(62)

3.1 History and Variety of Random Number Generation Methods

(6)

3.2 Traditional Quality Measures of Random Number Generators

(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

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Modern Statistical, Systems, and GPSS Simulation, Second Edition

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