An edition of Stationary stochastic models
(1990)
Stationary stochastic models
by Andreas Brandt
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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 arrival instants of customers and model continuity.
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Table of Contents
- 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.
- Bibliography
- Index
Edition Notes
Includes bibliographical references (p. [328]-339) and indexes.
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| November 29, 2023 | Edited by ImportBot | import existing book |
| April 30, 2023 | Edited by Kaustubh Chakraborty | Updated informations of the book |
| October 18, 2022 | Edited by ImportBot | import existing book |
| December 4, 2010 | Edited by Open Library Bot | Added subjects from MARC records. |
| December 10, 2009 | Created by WorkBot | add works page |