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Stochastic storage processes. Queues, insurance risk, dams, and data communication. 2nd ed. (English) Zbl 0888.60073
New York, NY: Springer. xvi, 206 p. (1997).
[For the first edition (1980) see Zbl 0453.60094.]
After an introduction, the book is structured in three parts. The first part is entitled “The single server queue” and contains three paragraphs. In this part there are presented the theory of single server queues with the first come first served discipline, using the fluctuation theory of the underlying random walk. The results obtained provide answers to most of the important questions for general systems, especially cases of Poisson arrivals, or systems with priority disciplines. Also, there are formulated storage models within the framework of continuous time. The second part, “Continuous time storage models”, presents the basic storage model. The class of models studied includes those for insurance risk and dams the underlying processes being a class of Lévy processes. One group of models is introduced with an integral equation and analyzed by special techniques that are available for this case. Also for general storage models the analysis uses the properties of ladder processes associated with the basic Lévy process. In the third part there are developed Markov-modulated storage processes arising in single-server queues and data communication models. So there are used the fluctuation theory of the underlying Markov-random walk. The treatment emphasizes the common features of the important problems. The book also contains problems and a selected bibliography, so it offers the possibility to be used as a course (textbook) on applied probability models. The material of this monograph represents the product of research carried out over a period of 40 years.

MSC:
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60K25 Queueing theory (aspects of probability theory)
60G50 Sums of independent random variables; random walks
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