A First Course in Stochastic Models

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.

The field of applied probability has changed profoundly in the pasttwenty years. The development of computational methods has greatlycontributed to a better understanding of the theory. A FirstCourse in Stochastic Models provides a self-containedintroduction to the theory and applications of stochastic models.Emphasis is placed on establishing the theoretical foundations ofthe subject, thereby providing a framework in which theapplications can be understood. Without this solid basis in theoryno applications can be solved.* Provides an introduction to the use of stochastic modelsthrough an integrated presentation of theory, algorithms andapplications.* Incorporates recent developments in computationalprobability.* Includes a wide range of examples that illustrate the modelsand make the methods of solution clear.* Features an abundance of motivating exercises that help thestudent learn how to apply the theory.* Accessible to anyone with a basic knowledge ofprobability.A First Course in Stochastic Models is suitable forsenior undergraduate and graduate students from computer scienceengineering, statistics, operations resear ch, and any otherdiscipline where stochastic modelling takes place. It stands outamongst other textbooks on the subject because of its integratedpresentation of theory, algorithms and applications.

Preface.The Poisson Process and Related Processes.Renewal-Reward Processes.Discrete-Time Markov Chains.Continuous-Time Markov Chains.Markov Chains and Queues.Discrete-Time Markov Decision Processes.Semi-Markov Decision Processes.Advanced Renewal Theory.Algorithmic Analysis of Queueing Models.Appendices.Appendix A: Useful Tools in Applied Probability.Appendix B: Useful Probability Distributions.Appendix C: Generating Functions.Appendix D: The Discrete Fast Fourier Transform.Appendix E: Laplace Transform Theory.Appendix F: Numerical Laplace Inversion.Appendix G: The Root-Finding Problem.References.Index.