Applied Stochastic System Modeling

Osaki, Shunji

ISBN 10: 3642846831 / ISBN 13: 9783642846830

Editore: Springer, 2011

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Dati bibliografici

• Titolo: Applied Stochastic System Modeling
• Editore: Springer
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 3642846831
• ISBN 13: 9783642846830
• Rilegatura: Paperback
• Condizione: Like New
• Tipo di libro: book

Descrizione articolo

Riassunto

The random phenomena can be described by stochastic processes. This book provides a systematic treatment of stochastic processes and their applications emphasizing the examples in engineering and management fields with numerous illustrations.

Contenuti

1 Probability Theory.- 1.1 Introduction.- 1.2 Sample Spaces and Events.- 1.3 Probabilities.- 1.4 Combinatorial Analysis.- 1.5 Problems 1.- 2 Random Variables and Distributions.- 2.1 Introduction.- 2.2 Random Variables and Distributions.- 2.3 Discrete Distributions.- 2.4 Continuous Distributions.- 2.5 Multivariate Distributions.- 2.6 Limit Theorems.- 2.7 Problems 2.- 3 Poisson Processes.- 3.1 Stochastic Processes.- 3.2 The Poisson Process.- 3.3 Interarrival Time Distributions.- 3.4 Conditional Waiting Time Distributions.- 3.5 Nonhomogeneous Poisson Processes.- 3.6 Problems 3.- 4 Renewal Processes.- 4.1 Introduction.- 4.2 Renewal Functions.- 4.3 Limit Theorems.- 4.4 Delayed and Stationary Renewal Processes.- 4.5 Problems 4.- 5 Discrete-Time Markov Chains.- 5.1 Introduction.- 5.2 Chapman-Kolmogorov Equation.- 5.3 State Classification.- 5.4 Limiting Probabilities.- 5.5 Finite-State Markov Chains.- 5.6 Problems 5.- 6 Continuous-Time Markov Chains.- 6.1 Introduction.- 6.2 Pure Birth Processes.- 6.3 Pure Death Processes.- 6.4 Birth and Death Processes.- 6.5 Finite-State Markov Chains.- 6.6 Problems 6.- 7 Markov Renewal Processes.- 7.1 Introduction.- 7.2 Markov Renewal Processes.- 7.3 Stationary Probabilities.- 7.4 Alternating Renewal Processes.- 7.5 Problems 7.- 8 Reliability Models.- 8.1 Introduction.- 8.2 Lifetime Distributions and Failure Rates.- 8.3 Availability Theory.- 8.4 Replacement Models.- 8.4.1 Age Replacement Models.- 8.4.2 Block Replacement Models.- 8.5 Ordering Models.- 8.5.1 Model I.- 8.5.2 Model II.- 8.6 Problems 8.- 9 Queueing Models.- 9.1 Introduction.- 9.2 Single Server Queueing Models.- 9.2.1 M/M/1/? Queueing Models.- 9.2.2 M/M/1/N Queueing Models.- 9.3 Multiple Server Queueing Models.- 9.3.1 M/M/c/?Queueing Models.- 9.3.2 M/M/c/c Queueing Models.- 9.3.3 M/M/?/? Queueing Models.- 9.4 Queues with a Finite Population.- 9.4.1 M/M/1/K/K Queueing Models.- 9.4.2 M/M/c/K/K Queueing Models.- 9.4.3 M/M/c/c/c Queueing Models.- 9.5 Problems 9.- A Laplace-Stieltjes Transforms.- A.1 Laplace-Stieltjes Transforms.- A.2 Properties of Laplace-Stieltjes Transforms.- A.3 Applications to Distributions.- A.4 Applications to Differential Equations.- A.5 Applications to Renewal Functions.- B Answers to Selected Problems.- C The Bibliography.