| Modern Statistical, Systems, and GPSS SimulationKarian, Z. A. and Dudewicz, E. J. |
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Table of Contents
Table of Contents1 Discrete Event Computer Simulation1.1 Computer Implementation of Simulations 1.2 The Single-Server Queue 1.2.1 A Single-Server Queueing Model 1.2.2 An Improved Model for the Single-Server Queue 1.2.3 Generation of Arrival Times and Other Attributes 1.3 The Single-Server Queue: Additional Goals 1.4 GPSS Model of the Single-Server Queue 1.5 Single-Server Queue with Priority Classes: Data Structures 1.5.1 Use of Ranked List Structures 1.5.2 Use of Floating File Structures 1.5.3 Linked-List Priority Queues 1.5.4 Double-Pointing Structures 1.6 Theoretical Results about the Single-Server Queue 1.6.1 Poisson Arrivals and Exponential Interarrival Times 1.6.2 Number of Customers in M/M/1/¥ Queueing Systems 1.6.3 Idle Time in M/M/l/¥ Queues 1.6.4 Expected Number of Customers in M/M/l/¥ Queues 1.6.5 Expected Number of Customers in the Facility and in the Queue of an M/M/l/¥ System 1.6.6 Expected Time Spent Waiting and in the System 1.6.7 Summary of Results and an Example 1.7 Use of Efficient Sorting Techniques in Simulation Problems for Chapter 1
2 Introduction to GPSS2.1 GPSS Program Structure 2.2 The SIMULATE, START, and END Statements 2.3 The GENERATE and TERMINATE Blocks 2.4 Facilities and the SEIZE and RELEASE Blocks 2.5 The ADVANCE Block 2.6 Queues and the QUEUE and DEPART Blocks 2.7 GPSS Program Output 2.8 Storages and the ENTER and LEAVE Blocks 2.9 The TRANSFER Block 2.10 Example: An Appliance Repair Shop Problems for Chapter 2
3 Random Number Generation and Testing3.1 History and Variety of Random Number Generation Methods 3.2 Traditional Quality Measures of Random Number Generators 3.3 Statistical Quality Measures of Random Number Generators 3.3.1 Uniformity of Distribution Test 3.3.2 Coupon Collector's Test 3.3.3 Gap Test 3.3.4 Permutation Test 3.3.5 Poker Test 3.3.6 Runs-Up Test 3.3.7 Serial Pairs Test 3.3.8 Chi-Square on Chi-Squaxes Test (CSCS Test) 3.3.9 Entropy-Uniformity Test 3.4 Theoretical Tests of Random Number Generators 3.4.1 Serial Correlation Test 3.4.2 Interplanar Distance (or Spectral) Test 3.5 Test Results on Specific Random Number Generators 3.5.1 Random Number Generators 3.5.2 Tests of Random Number Generators and Their Results 3.6 Notes on the Use of TESTRAND Problems for Chapter 3
4 Random Variable Generation4.1 Selection of a Distribution 4.2 Generating Univariate Random Variables: Inverse Distribution Function Method 4.2.1 The Exponential Distribution 4.2.2 The Bernoulli Distribution 4.2.3 The Normal Distribution 4.2.4 The Uniform Distribution 4.2.5 The Binomial Distribution 4.3 Generating Univariate Random Variables: Discrete Distributions 4.4 Generating Poisson and Geometric Random Variables
4.4.1 The Poisson Distribution 4.4.2 The Geometric Distribution 4.5 Generating Bivariate and Multivariate Discrete Distributions 4.6 Generating Specific Univariate Distributions 4.6.1 The Binomial Distribution 4.6.2 The Normal Distribution 4.6.3 The Chi-Square Distribution 4.6.4 Student's t-Distribution 4.6.5 The Erlang Distribution 4.6.6 Double-Exponential Distribution: Via Exponential 4.6.7 The F Distribution: Via Chi-Squares 4.6.8 The Beta Distribution 4.6.9 The Weibull Distribution: Via the Exponential 4.6.10 The Lognormal Distribution: Via the Normal 4.6.11 The Gamma Distribution 4.7 Generating p.d.f.s Bounded on a Closed Interval 4.8 Generating Multivariate Normal Random Variables 4.9 Confidence Regions for Multivariate Normal Random Variables 4.10 Fitting Distributions to Data: The GLD Family, Univariate and Bivariate 4.10.1 The Parameter Space of the GLD 4.10.2 Estimation of the GLD Parameters 4.10.3 The Extended GLD 4.10.4 Bivariate GLD Distribution: The GLD-2 4.11 Empiric Distribution Function and Empiric p.d.f 4.12 Sampling from a Histogram 4.13 Fitting a Normal (Univariate or Multivariate) Distribution Problems for Chapter 4
5 Intermediate GPSS5.1 Transaction Movement 5.2 The START Statement and Chain Output 5.3 Random Number Generators Built into GPSS 5.4 The RESET, RMULT, and CLEAR Control Statements 5.5 GPSS Functions 5.5.1 Discrete Functions 5.5.2 Continuous Functions 5.6 Example. A Manufacturing Shop 5.7 Sampling: The Exponential Distribution 5.8 Arithmetic Variables in GPSS 5.9 Sampling: The Normal Distribution 5.10 Transaction Parameters and the ASSIGN Block 5.11 Example: A Batch Computer System Operation Problems for Chapter 5
6 Statistical Design and Analysis of Simulations6.1 How Long to Simulate: Goal of Estimating the Mean 6.1.1 The Proportional Closeness Goal 6.1.2 Case Study of Estimating Demand for Emergency Services 6.2 How Long to Simulate: Estimating the Difference m1 - m2 6.3 How Long to Simulate: Goal of Selection of the Best 6.4 System Optimization via Statistical Design and Regression 6.4.1 Example: A Time-Shared Computer System 6.4.2 Central Composite Design for k = 2 Variables 6.5 Statistical Simulation and the "Bootstrap" Method 6.6 The Generalized Bootstrap 6.7 Other Statistical Design and Analysis Aspects of Simulation 6.7.1 Estimation of a Percentile Point 6.7.2 Estimation of Var(x) 6.7.3 Variance Reduction Techniques Problems for Chapter 6
7 Advanced GPSS Features7.1 Standard Numerical Attributes 7.1.1 Facilities 7.1.2 Queues 7.1.3 Storages 7.1.4 Blocks 7.1.5 Transactions 7.1.6 The Clock 7.1.7 Other SNAs 7.2 Savevalues, the INITIAL Statement, and the SAVEVALUE Block 7.2.1 The INITIAL Statement 7.2.2 The SAVEVALUE Block 7.3 Example: A Repair Service Operation 7.4 The PRINT Block 7.5 Example: Demand Estimation 7.6 User-Defined Random Number Generators 7.7 Transit Time and the MARK Block 7.8 The TABLE Statement and the TABULATE Block 7.8.1 The TABLE Statement 7.8.2 The TABULATE Block 7.8.3 Variations of the TABLE Statement 7.9 The PRIORITY, PREEMPT, and RETURN Blocks 7.9.1 The PRIORITY Block 7.9.2 The PREEMPT and RETURN Blocks 7.9.3 Preempted Transactions 7.10 Example: Emergency Medical System 7.11 SNA Comparisons and the TEST Block 7.12 Example: A Time-Shared Computer System 7.13 The LOOP Block 7.14 Logic Switches, INITIAL Statements, LOGIC and GATE Blocks 7.14.1 Initialization of Logic Switches 7.14.2 The LOGIC Block 7.14.3 Logic Switches and the GATE Block 7.14.4 Other Forms of the GATE block 7.15 The SELECT Block 7.15.1 The Relational Mode 7.15.2 The Min-Max Mode 7.15.3 The Logical Mode 7.16 Example: A Multiple-Checkout Supermarket Operation 7.17 User Chains and the LINK and UNLINK Blocks Problems for Chapter 7
8 Case Study of a Simulation: Design, Analysis, Programming8.1 Description of the Transportation System Problem 8.2 Statistical Design 8.2.1 Statistically Designed Experimentation 8.2.2 Naive Experimentation 8.3 Statistical Analysis 8.3.1 Analysis of Data 8.3.2 Statistical Programming in SAS for Data Analysis 8.4 The GPSS Program 8.4.1 Functions, Variables, and Savevalues 8.4.2 The Program Logic 8.4.3 Program Output Problems for Chapter 8
AppendicesA Using GPSS/PC A.1 Running a GPSS/PC Program A.2 Interacting with GPSS/PC A.3 GPSS/PC Output A.4 The GPSS/PC Models on the Disk A.5 Debugging in GPSS/PC B GPSS Block Statement Formats C The Normal Distribution D The Student's t-Distribution E The Chi-Square Distribution F The Chi-Square Distribution with 99 Degrees of Freedom G Random Numbers H Tables for Selection of the Best |
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