Probability, Markov Chains, Queues, and Simulation : The Mathematical Basis of Performance Modeling / William J. Stewart.

Format:

Book

Author/Creator:

Stewart, William J., Author.

Language:

English

Subjects (All):

Probabilities--Computer simulation.

Probabilities.

Markov processes.

Queuing theory.

Physical Description:

1 online resource (777 p.)

Place of Publication:

Princeton, NJ : Princeton University Press, [2009]

Language Note:

English

Summary:

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 set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov 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 birth-death processes are analyzed in detail, as are queues with phase-type 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

Contents:

Frontmatter

Contents

Preface and Acknowledgments

Part I: PROBABILITY

Chapter 1. Probability

Chapter 2. Combinatorics-The Art of Counting

Chapter 3. Random Variables and Distribution Functions

Chapter 4. Joint and Conditional Distributions

Chapter 5. Expectations and More

Chapter 6. Discrete Distribution Functions

Chapter 7. Continuous Distribution Functions

Chapter 8. Bounds and Limit Theorems

Part II: MARKOV CHAINS

Chapter 9. Discrete- and Continuous-Time Markov Chains

Chapter 10. Numerical Solution of Markov Chains

Part III. QUEUEING MODELS

Chapter 11. Elementary Queueing Theory

Chapter 12. Queues with Phase-Type Laws: Neuts' Matrix-Geometric Method

Chapter 13. The z-Transform Approach to Solving Markovian Queues

Chapter 14. The M/G/1 and G/M/1 Queues

Chapter 15. Queueing Networks

Part IV: SIMULATION

Chapter 16. Some Probabilistic and Deterministic Applications of Random Numbers

Chapter 17. Uniformly Distributed "Random" Numbers

Chapter 18. Nonuniformly Distributed "Random" Numbers

Chapter 19. Implementing Discrete-Event Simulations

Chapter 20. Simulation Measurements and Accuracy

Appendix A: The Greek Alphabet

Appendix B: Elements of Linear Algebra

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references (pages [745]-747) and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Nov 2019)

ISBN:

9781400832811

1400832810

OCLC:

756484370