Vidyadhar G. Kulkarni

Modeling and Analysis of Stochastic Systems

• Gebundenes Buch

Produktbeschreibung

Table of contents:
Introduction. Discrete-Time Markov Chains: Transient Behavior. Discrete-Time Markov Chains: Limiting Behavor. Discrete-Time Markov Chains: First Passage Times. Poisson Processes
Continuous-Time Markov Chains. Applications of Markov Chains to Queueing Theory. Renewal Processes. Markov Renewal Processes
Epilogue. Appendices. Answers to Selected Problems. Bibliography.

Produktdetails

• Verlag: Springer US, Norwell
• Englisch
• ISBN-13: 9780412049910
• ISBN-10: 0412049910
• Artikelnr.: 22449707

Inhaltsangabe

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