Book Description
Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics.
The textbook looks at the fundamentals of probability theory, from the basic concepts of setbased probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuoustime Markov chains are analyzed from a theoretical and computational point of view. Topics include the ChapmanKolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birthdeath processes are analyzed in detail, as are queues with phasetype arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation.
Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only).
 Numerous examples illuminate the mathematical theories
 Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach
 Each chapter concludes with an extensive set of exercises
Table of Contents
 Cover
 Half title
 Title
 Copyright
 Dedication
 Contents
 Preface and Acknowledgments

I Probability
 1 Probability
 2 Combinatorics—The Art of Counting

3 Random Variables and Distribution Functions
 3.1 Discrete and Continuous Random Variables
 3.2 The Probability Mass Function for a Discrete Random Variable
 3.3 The Cumulative Distribution Function
 3.4 The Probability Density Function for a Continuous Random Variable
 3.5 Functions of a Random Variable
 3.6 Conditioned Random Variables
 3.7 Exercises
 4 Joint and Conditional Distributions
 5 Expectations and More
 6 Discrete Distribution Functions
 7 Continuous Distribution Functions
 8 Bounds and Limit Theorems

II Markov Chains

9 Discrete and ContinuousTime Markov Chains
 9.1 Stochastic Processes and Markov Chains
 9.2 DiscreteTime Markov Chains: Definitions
 9.3 The ChapmanKolmogorov Equations
 9.4 Classification of States
 9.5 Irreducibility
 9.6 The Potential, Fundamental, and Reachability Matrices
 9.7 Random Walk Problems
 9.8 Probability Distributions
 9.9 Reversibility
 9.10 ContinuousTime Markov Chains
 9.11 SemiMarkov Processes
 9.12 Renewal Processes
 9.13 Exercises

10 Numerical Solution of Markov Chains
 10.1 Introduction
 10.2 Direct Methods for Stationary Distributions
 10.3 Basic Iterative Methods for Stationary Distributions
 10.4 Block Iterative Methods
 10.5 Decomposition and Aggregation Methods
 10.6 The Matrix Geometric/Analytic Methods for Structured Markov Chains
 10.7 Transient Distributions
 10.8 Exercises

9 Discrete and ContinuousTime Markov Chains

III Queueing Models

11 Elementary Queueing Theory
 11.1 Introduction and Basic Definitions
 11.2 BirthDeath Processes: The M/M/1 Queue
 11.3 General BirthDeath Processes
 11.4 Multiserver Systems
 11.5 FiniteCapacity Systems—The M/M/1/K Queue
 11.6 Multiserver, FiniteCapacity Systems—The M/M/c/K Queue
 11.7 FiniteSource Systems—The M/M/c//M Queue
 11.8 StateDependent Service
 11.9 Exercises

12 Queues with PhaseType Laws: Neuts’ MatrixGeometric Method
 12.1 The Erlangr Service Model—The M/Er/1 Queue
 12.2 The Erlangr Arrival Model—The Er/M/1 Queue
 12.3 The M/H2/1 and H2/M/1 Queues
 12.4 Automating the Analysis of SingleServer PhaseType Queues
 12.5 The H2/E3/1 Queue and General Ph/Ph/1 Queues
 12.6 Stability Results for Ph/Ph/1 Queues
 12.7 Performance Measures for Ph/Ph/1 Queues
 12.8 Matlab code for Ph/Ph/1 Queues
 12.9 Exercises
 13 The zTransform Approach to Solving Markovian Queues

14 The M/G/1 and G/M/1 Queues
 14.1 Introduction to the M/G/1 Queue
 14.2 Solution via an Embedded Markov Chain
 14.3 Performance Measures for the M/G/1 Queue
 14.4 The M/G/1 Residual Time: Remaining Service Time
 14.5 The M/G/1 Busy Period
 14.6 Priority Scheduling
 14.7 The M/G/1/K Queue
 14.8 The G/M/1 Queue
 14.9 The G/M/1/K Queue
 14.10 Exercises
 15 Queueing Networks

11 Elementary Queueing Theory

IV Simulation
 16 Some Probabilistic and Deterministic Applications of Random Numbers
 17 Uniformly Distributed “Random” Numbers
 18 Nonuniformly Distributed “Random” Numbers
 19 Implementing DiscreteEvent Simulations
 20 Simulation Measurements and Accuracy
 Appendix A: The Greek Alphabet
 Appendix B: Elements of Linear Algebra
 Bibliography
 Index
Product Information
 Title: Probability, Markov Chains, Queues, and Simulation
 Author(s):
 Release date: July 2009
 Publisher(s): Princeton University Press
 ISBN: 9781400832811