Stationary stochastic models
著者
書誌事項
Stationary stochastic models
（Wiley series in probability and mathematical statistics, . Probability and mathematical statistics）
Wiley, c1990
大学図書館所蔵 全55件
注記
Bibliography: p. [328]-339
Includes indexes
内容説明・目次
内容説明
Looking at the stochastic modelling of systems, this book examines one of the basic problems with such modelling - the existence and uniqueness of stationary (limiting) distributions of system characteristics. The book looks at topics such as the arrival instants of customers in a queue, model continuity and insensitivity of stationary distributions concerning the form of the distribution functions of certain input characteristics. These problems have been traditionally treated by means of Markov, renewal, and Markov renewal processes, which the authors claim are often not adequate for these problems.
目次
- Recursive stochastic equations - weak and strong solutions - ergodic weak solutions - construction of stationary weak and strong solutions - Wald's identity for dependent random variables - model continuity in the presence of renewing epochs - method of metric modification - continuity of weak solutions
- the case of stationary Markov chains
- stationary sequences and stationary marked point processes - ergodic marked point processes
- continuous time models - stochastic processes with an embedded point process - semi-Markov and semi-regenerative processes - continuous time state processes - recursive stochastic equations in continuous time
- arrival-stationary queuing processes: existence and uniqueness - notations - the system - single server queue - the system with FCFS queueing discipline - the system with cyclic queueing discipline - the single server queue with warming-up - the many server loss system with repeated call attempts - open networks of loss systems
- relationships between arrival, time and departure stationary queueing processes - Poisson arrivals see time averages (PASTA) - the number of customers - the busy cycle - Takaes' and Pollaczek-Khinchin formulae
- batch-arrival stationary queuing processes - the system with geometrically distributed batch size - constant batch size - single server queue with batch arrivals - feedback queues - comparing batch delays and customer delays
- continuity of queueing models
- further models - the stochastic equation with stationary coefficients - stability of robust filter cleaners - non-contractivity of the filters - a further method for constructing solutions of recursive stochastic equations - the filter with fixed scale - variable scale.
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