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Introduction to queueing theory. (Vvedenie v teoriyu massovogo obsluzhivaniya). 2nd ed., rev. and compl. (Russian) Zbl 0624.60108

Fiziko-Matematicheskaya Biblioteka Inzhenera. Moskva: “Nauka”. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 336 p. R. 1.60 (1987).
This is the second (revised) edition of the book. In order to give an impression of its contents we list the titles of the chapters with short comments. Chapter 1 “Problems of queueing systems under the simplest conditions” contains the analysis of Poisson flows, birth and death processes, Markov queues. Chapter 2 “Input flows” is devoted to different results concerning input flows: non-stationary Poisson flows, general stationary flows, limit theorems for sums of random flows and their rarification. It contains also elements of renewal theory.
Chapter 3 “Some classes of random processes” considers the following types of processes: imbedded Markov chains, semi-Markov processes, piecewise linear Markov processes, Markov processes with supplementary variables.
Chapter 4 “Semi-Markov queueing models” contains the analysis of some concrete models: M/G/1, GI/M/m, priority queues and some others. “Application of more general methods” is the topic of Chapter 5 which contains the applications of renewal theory, Markov processes with supplementary variables, random walks, integro-differential equations to GI/G/1, GI/G/m, M/G/m/0 and some other queues. There is a piece of material on stability of queues and their ergodic properties. Chapter 6 is devoted to “Monte Carlo simulation”. Apart from traditional material it contains new results on calculating small probabilities via simulation.
Reviewer: V.Kalashnikov

MSC:

60K25 Queueing theory (aspects of probability theory)
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
90B22 Queues and service in operations research
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
65C99 Probabilistic methods, stochastic differential equations