Chapter 6 Introduction to Queueing Theory
6.1 Introduction 6.2 Specification of Queueing Models 6.2.1 Stochastic Models for Arrival and Service Processes 6.2.2 Structural Parameters 6.2.3 Operating Policies 6.2.4 The A/B/m /K Notation 6.2.5 Open and Closed Queueing Systems 6.3 Performance of a Queuing System 6.4 Queueing System Dynamics 6.5 Little's Law 6.6 Analysis of Simple Markovian Queueing Systems 6.6.1 The M/M/1 Queueing System 6.6.2 The M/M/m Queueing System 6.6.3 The M/M/ Queueing System 6.6.4 The M/M/1/K Queueing System 6.6.5 The M/M/m/m Queueing System 6.6.6 The M/M/1//N Queueing System 6.6.7 The M/M/m/K/N Queueing System 6.7 Markovian Queueing Networks 6.7.1 The Departure Process of the M/M/1 Queueing System 6.7.2 Open Queueing Networks 6.7.3 Closed Queueing Networks Computation of the Normalization Constant C(N) Mean Value Analysis 6.7.4 Product Form Networks 6.8 Non-Markovian Queueing Systems 6.8.1 The Method of Stages 6.8.2 Mean Value Analysis of the M/G/1 Queueing System 6.8.3 Software Tools for the Analysis of General Queueing Networks
Chapter 7 Controlled Markov Chains
7.1 Introduction 7.2 The Nature of "Control" in Markov Chains 7.3 Markov Decision Processes 7.3.1 Cost Criteria 7.3.2 Uniformization 7.3.3 The Basic Markov Decision Problem 7.4 Solving Markov Decision Problems 7.4.1 The Basic Idea of Dynamic Programming 7.4.2 Dynamic Programming and the Optimality Equation Convergence of the Dynamic Programming Algorithm The Optimality Equation 7.4.3 Extensions to Unbounded and Undiscounted Costs 7.4.4 Optimization of the Average Cost Criterion 7.5 Control of Queueing Systems 7.5.1 The Admission Problem 7.5.2 The Routing Problem 7.5.3 The Scheduling Problem
Chapter 8 Introduction to Discrete-Event Stimulation
8.1 Introduction 8.2 The Event Scheduling Simulation Scheme 8.2.1 Simulation of a Simple Queueing System 8.3 The Process-Oriented Simulation Scheme 8.4 Discrete-Event Simulation Languages 8.5 Discrete-Event Simulation Using the Siman Language 8.5.1 The MODEL File - Some Basic Block Functions 8.5.2 The MODEL File - Some Data Collection Block Functions 8.5.3 The EXPERIMENT File 8.5.4 More Elaborate Models 8.5.5 Common Mistakes 8.6 Random Number Generation 8.6.1 The Linear Congruential Technique 8.7 Random Variate Generation 8.7.1 The Inverse Transform Technique 8.7.2 The Convolution Technique 8.7.3 The Composition Technique 8.7.4 The Acceptance - Rejection Technique 8.8 Output Analysis 8.8.1 Simulation Characterizations 8.8.2 Parameter Estimation Point Estimation Interval Estimation 8.8.3 Output Analysis of Terminating Simulations 8.8.4 Output Analysis of Non-Terminating Simulations Replications with Deletions Batch Means Regenerative Simulation
Chapter 9 Sensitivity Analysis and Sample Path Constructability
9.1 Introduction 9.2 Sample Functions and Their Derivatives 9.2.1 Performance Sensitivities 9.2.2 The Uses of Sensitivity Information 9.3 Perturbation Analysis: Some Key Ideas 9.4 Perturbation Analysis of GI/G/1 Queueing Systems 9.4.1 Perturbation Generation Derivatives of Random Variated Scale and Location Parameters Parameters of Discrete Distributions 9.4.2 Perturbation Propagation Infinitesimal and Finite Perturbaton Analysis 9.4.3 Infinitesimal Perturbation Analysis (IPA) 9.4.4 Implementation of IPA for the GI/G/1 System 9.5 IPA for Stochastic Time Automata 9.5.1 Event Time Derivatives 9.5.2 Sample Function Derivatives 9.5.3 Performance Measure Derivatives The Commuting Condition Continuity of Sample Functions Unbiasedness of IPA Estimators 9.5.4 IPA Applications Sensitivity Analysis of Queueing Networks Performance Optimization 9.6 The Sensitivity Estimation Problem Revisited 9.7 Extensions of IPA 9.7.1 Discontinuities due to Multiple Customer Classes 9.7.2 Discontinuities due to Touting Decisions 9.7. Discontinuities due to Blocking: IPA with Event Rescheduling 9.8 Smoothed Perturbation Analysis (SPA) 9.8.1 Systems with Real-Time Constraints 9.8.2 Marking and Phantomizing Techniques 9.9 Perturbation Analysis for Finite Parameter Changes 9.10 Sample Path Constructability Techniques