Modeling and Analysis of Stochastic Systems / Edition 3

by Vidyadhar G. Kulkarni

Overview

Building on the author’s more than 35 years of teaching experience, Modeling and Analysis of Stochastic Systems, Third Edition, covers the most important classes of stochastic processes used in the modeling of diverse systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models.

The third edition has been updated with several new applications, including the Google search algorithm in discrete time Markov chains, several examples from health care and finance in continuous time Markov chains, and square root staffing rule in Queuing models. More than 50 new exercises have been added to enhance its use as a course text or for self-study. The sequence of chapters and exercises has been maintained between editions, to enable those now teaching from the second edition to use the third edition.

Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, readers will be well-equipped to build and analyze useful stochastic models for real-life situations.

Product Details

ISBN-13:	9781498756617
Publisher:	Taylor & Francis
Publication date:	10/07/2016
Series:	Chapman & Hall/CRC Texts in Statistical Science
Edition description:	Revised
Pages:	606
Product dimensions:	6.40(w) x 9.30(h) x 1.40(d)

About the Author

Vidyadhar G. Kulkarni

Table of Contents

IntroductionWhat in the World is a Stochastic Process? How to Characterize a Stochastic ProcessWhat Do We Do with a Stochastic Process? Discrete-Time Markov Chains: Transient BehaviourDefinition and CharacterizationExamplesDTMCs in Other FieldsMarginal DistributionsOccupancy TimesComputation of Matrix PowersModeling ExercisesComputational ExercisesConceptual ExercisesDiscrete-Time Markov Chains: First Passage TimesDefinitionsCumulative Distribution Function of TAbsorption ProbabilitiesExpectation of TGenerating Function and Higher Moments of TComputational ExercisesConceptual ExercisesDiscrete-Time Markox Chains: Limiting BehaviourExploring the Limiting Behaviour by ExamplesClassification of StatesDetermining Recurrence and Transience: Finite DTMCsDetermining Recurrence and Transience: Infinite DTMScLimiting Behaviour of Irreducible DTMCsExamples: Limiting Behaviour of Infinite State-Space Irreducible DTMCsLimiting Behaviour of Reducible DTMCsDTMCs with Costs and RewardsReversibilityComputational ExercisesConceptual ExercisesPoisson ProcessesExponential DistributionsPoisson Process: DefinitionsEvent Times in a Poisson ProcessSuperposition and Splitting of Poisson ProcessesNon-Homogeneous Poisson ProcessCompound Poisson ProcessComputational ExercisesConceptual ExercisesContinuous-Time Markov ChainsDefinitions and Sample Path PropertiesExamplesCTMCs in Other FieldsTransient Behaviour: Marginal DistributionTransient Behaviour: Occupancy TimesComputation of P(t): Finite State-SpaceComputation of P(t): Infinite State-SpaceFirst-Passage TimesExploring the Limiting Behaviour by ExamplesClassification of StatesLimiting Behaviour of Irre

Editorial Reviews

"The third edition of Modeling and Analysis of Stochastic Systems remains an excellent book for a graduate-level study of stochastic processes. The aim of the book is modeling with stochastic elements in practical settings and analysis of the resulting stochastic model. The target audience is quantitative disciplines such as operations research, statistics, computer science, economics, and others where the book is well positioned, since it is application-driven and does not require measure theoretic probability. … The numerous exercises, separated into modeling, computational, and conceptual classes, are a strength of this text. The author also notes that most come from his own homework and exams, making them a valuable resource."
—James M. Flegal, University of California, Riverside, in Journal of the American Statistical Association, January 2018

From the Publisher

A practical text that enables students in engineering, business, operations research, public policy, and computer science to model and analyze stochastic systems. The major cases of useful stochastic processes--discrete and continuous time Markov chains, renewal processes, regenerative processes, and Markov regenerative processes--are presented, with an emphasis on modeling real-life situations with stochastic elements and analyzing the resulting stochastic model. Includes numerous worked examples and exercises. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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