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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.
List 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
About the author
Vidyadhar G. Kulkarni
