Contents

Sample Path Analysis and Simulation of Stochastic Systems

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Chapters: 7
Pages: 48

Chapter 1Introduction

1.1 Motivation and Overview
1.2 Exponential and Poisson Distribution
1.3 Fighting the Exponential Distribution is Futile
1.4 Probabilistic Arithmetic

Chapter 2Construction of Simple Discrete-time Stochastic Processes

Introduction
2.1 Waiting for a Psychiatrist
2.2 Simulating the Psychiatrists Case
2.3 General Behavior of Queueing Systems
2.4 Queueing Processes as Regulated Random Walks
2.5 Control of Single-item Inventory Systems
2.6 Simulating Single-Item Inventory Systems

Chapter 3Construction of Simple Continuous-time Stochastic Processes

Introduction
3.1 Queueing Process in Continuous Time
3.2 Kendall's Notation
3.3 Simulating Waiting Times
3.4 Simulation of Queue Length with Heap Queues
3.5 Discrete-event Simulation
3.6 Discrete-Event Simulations: Examples

Chapter 4Fundamental Tools

Introduction
4.1 Rate, Stability and Load
4.2 (Limits of) Empirical Performance Measures
4.3 Renewal Reward Theorem
4.4 Little's Law
4.5 Poisson Arrivals See Time Averages
4.6 Level Crossing and Balance Equations
4.7 Graphical Summaries

Chapter 5Exact Models

Introduction
5.1 The \(M(n)/M(n)/1\) Queue
5.2 Applications of the \(M(n)/M(n)/1\) queueing model
5.3 \(M^B/M/1\) Queue and Rejection Policies
5.4 \(M/G/1\) Queue: Expected Waiting Time
5.5 \(M/G/1\) Queue Length Distribution
5.6 \(N\)-policies for the \(M/G/1\) Queue
5.7 Analytic Results for the Base-Stock Policy
5.8 Analytic Results for the \((Q,r)\) Policy
5.9 An algorithm for the \((s, S)\) and \((T, S)\) policies
5.10 Hitting problems with applications in single-item inventory control

Chapter 6Approximate Models

Introduction
6.1 The \(G/G/c\) Queue
6.2 Server Setups
6.3 Server Adjustments
6.4 Server Failures

Chapter 7Queueing Networks

Introduction
7.1 \(G/G/c\) Queues in Tandem
7.2 Deterministic Queueing Networks
7.3 Open Single-Class Product-Form Networks
7.4 On \(\lambda = \gamma + \lambda P\)

Notation

notation

CC BY-SA 4.0. Sample Path Analysis and Simulation of Stochastic Systems by Nicky D. van Foreest is licensed by the University of Groningen under a Creative Commons Attribution-ShareAlike 4.0 International License.