A first course in stochastic models

Henk C. Tijms0471498807, 9780471498803, 0471498815, 9780471498810, 9780470864289

The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. A First Course in Stochastic Models provides a self-contained introduction to the theory and applications of stochastic models. Emphasis is placed on establishing the theoretical foundations of the subject, thereby providing a framework in which the applications can be understood. Without this solid basis in theory no applications can be solved. Provides an introduction to the use of stochastic models through an integrated presentation of theory, algorithms and applications. Incorporates recent developments in computational probability. Includes a wide range of examples that illustrate the models and make the methods of solution clear. Features an abundance of motivating exercises that help the student learn how to apply the theory. Accessible to anyone with a basic knowledge of probability.
A First Course in Stochastic Models is suitable for senior undergraduate and graduate students from computer science, engineering, statistics, operations resear ch, and any other discipline where stochastic modelling takes place. It stands out amongst other textbooks on the subject because of its integrated presentation of theory, algorithms and applications.

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Table of contents :
Cover Page……Page 1
Title Page……Page 2
Copyright 2003 John Wiley & Sons Ltd……Page 3
3 Discrete-Time Markov Chains……Page 4
5 Markov Chains and Queues……Page 5
9 Algorithmic Analysis of Queueing Models……Page 6
Index……Page 7
Preface……Page 8
1 The Poisson Process and Related Processes……Page 9
2 Renewal-Reward Processes……Page 41
3 Discrete-Time Markov Chains……Page 88
4 Continuous-Time Markov Chains……Page 147
5 Markov Chains and Queues……Page 193
6 Discrete-Time Markov Decision Processes……Page 239
7 Semi-Markov Decision Processes……Page 284
8 Advanced Renewal Theory……Page 311
9 Algorithmic Analysis of Queueing Models……Page 343
Appendix A. Useful Tools in Applied Probability……Page 435
Appendix B. Useful Probability Distributions……Page 444
Appendix C. Generating Functions……Page 453
Appendix D. The Discrete Fast Fourier Transform……Page 459
Appendix E. Laplace Transform Theory……Page 462
Appendix F. Numerical Laplace Inversion……Page 466
Appendix G. The Root-Finding Problem……Page 474
References……Page 478
Index……Page 479