Applied Probability and Queues.

Abstract

This book treats the mathematics of queueing theory and some related areas, as well as the basic mathematical tools for the study of such models.It thus aims to serve as an introduction to queueing theory, to provide a thorough treatment of tools such as Markov processes, renewal theory, random walks, Lévy processes, matrix-analytic methods and change of measure, and to treat in some detail basic structures such as the GI/G/1 and GI/G/s queues, Markov-modulated models, queueing networks, and models within the areas of storage, inventory and insurance risk.Within this framework the choice of topics is, however, rather traditional.The aim has been to present what I consider the basic knowledge in the area, not to advocate special directions in which the area is at present developing.The first edition was published in 1987.This second edition incorporates about 100 extra pages containing an extended treatment of queueing networks and matrix-analytic methods as well as a number of additional topics, in particular Poisson's equation, the fundamental matrix, insensitivity, rare events and extreme values for regenerative processes, Palm theory, rate conservation, Lévy processes, reflection, Skorokhod problems, Loynes's lemma, Siegmund duality, light traffic, heavy tails, the Ross conjecture and ordering, and finite buffer problems.Also, the references, typically given in the Notes following the separate sections, have been thoroughly updated.It should be noted, however, that these Notes are mainly intended as a first guidance for further reading, not as a bibliography or history of the subject.When a textbook or a survey paper dealing with a topic is available, this is the preferred reference rather than the original papers.Thus, details of priority are treated rather sporad-

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