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Titlebook: Introduction to Stochastic Networks; Richard Serfozo Book 1999 Springer Science+Business Media New York 1999 BCMP network.Computer.Jackson

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发表于 2025-3-21 16:28:36 | 显示全部楼层 |阅读模式
书目名称Introduction to Stochastic Networks
编辑Richard Serfozo
视频video
丛书名称Stochastic Modelling and Applied Probability
图书封面Titlebook: Introduction to Stochastic Networks;  Richard Serfozo Book 1999 Springer Science+Business Media New York 1999 BCMP network.Computer.Jackson
描述In a stochastic network, such as those in computer/telecommunications and manufacturing, discrete units move among a network of stations where they are processed or served. Randomness may occur in the servicing and routing of units, and there may be queueing for services. This book describes several basic stochastic network processes, beginning with Jackson networks and ending with spatial queueing systems in which units, such as cellular phones, move in a space or region where they are served. The focus is on network processes that have tractable (closed-form) expressions for the equilibrium probability distribution of the numbers of units at the stations. These distributions yield network performance parameters such as expectations of throughputs, delays, costs, and travel times. The book is intended for graduate students and researchers in engineering, science and mathematics interested in the basics of stochastic networks that have been developed over the last twenty years. Assuming a graduate course in stochastic processes without measure theory, the emphasis is on multi-dimensional Markov processes. There is also some self-contained material on point processes involving real
出版日期Book 1999
关键词BCMP network; Computer; Jackson network; Kelly network; Markov process; Poisson process; Probability distr
版次1
doihttps://doi.org/10.1007/978-1-4612-1482-3
isbn_softcover978-1-4612-7160-4
isbn_ebook978-1-4612-1482-3Series ISSN 0172-4568 Series E-ISSN 2197-439X
issn_series 0172-4568
copyrightSpringer Science+Business Media New York 1999
The information of publication is updating

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发表于 2025-3-21 21:03:49 | 显示全部楼层
Reversible Processes, expected number of the transitions in the reverse order. This is also equivalent to a time-reversibility property that, at any instant, the future of the process is stochastically indistinguishable from viewing the process in reverse time. A remarkable feature of such a process is that its equilibr
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Miscellaneous Networks,e processes to model networks with multiple types of units, where the routings and services may depend on a customer’s type. This includes Kelly networks with deterministic routes for units, and BCMP networks with Cox and general service times depending on a unit’s type. We also discuss several form
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Little Laws,ttle law. Specifically, a Little law for a service system says that the average sojourn time . of a customer in the system and the average queue length . of the system are related by . = λ., where λ is the average arrival rate of units to the system. This fundamental relation is a . or law of large
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Stationary Systems,ulus and Campbell—Mecke formulas for functionals of stationary systems. This material is the foundation for modeling networks and queueing systems with stationary dynamics, and for obtaining Little laws for such systems.
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,Space—Time Poisson Models,the collective movement of units or customers in space and time, where the units enter the system according to a Poisson space—time process and then move about independently of each other. Because of these properties, the evolution of the system can be formulated by certain “random transformations”
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Spatial Queueing Systems, or a general space. The state of such a system is a point process on a space that evolves over time as a “measure-valued” Markov jump process. Each unit moves in the space according to a Markovian routing mechanism and it receives services at the locations it visits. The service times are exponenti
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