##
**The single server queue.
2nd impression of the 2nd revised ed. 1982.**
*(English)*
Zbl 0746.60093

North-Holland Series in Applied Mathematics and Mechanics. 8. Amsterdam etc.: North-Holland. xiv, 694 p. (1992).

[For the 2nd revised edition (1982) see Zbl 0481.60003 and for the first edition (1969) see Zbl 0183.49204.]

The book consists of three parts. The first part gives main notions and results from the general theory of stochastic processes which are necessary for queueing theory: Markov chains, birth and death processes, regenerate processes, ergodicity, stationary distributions, taboo probabilities. In the second part the classical single channel queueing system is considered. The author investigates all main processes associated with this system (queue length, waiting time, busy period, departure flow) under various assumptions about input flow and service time distribution (\(M/M\), \(G/M\), \(M/G\), \(G/G\) models). Methods which are used in this part are quite general and in fact this part can be considered as a very good textbook on the calssical queueing theory. In the third part some complicated variants of the above classical single channel queue are considered: the bulk queue, priority queues, etc.

The book covers almost all general methods in the theory of single line queueing models. It is of extreme interest for applied mathematicians, computer, electrical and industrial engineers, operations researchers working in queueing theory or using methods and results of the queueing theory.

The book consists of three parts. The first part gives main notions and results from the general theory of stochastic processes which are necessary for queueing theory: Markov chains, birth and death processes, regenerate processes, ergodicity, stationary distributions, taboo probabilities. In the second part the classical single channel queueing system is considered. The author investigates all main processes associated with this system (queue length, waiting time, busy period, departure flow) under various assumptions about input flow and service time distribution (\(M/M\), \(G/M\), \(M/G\), \(G/G\) models). Methods which are used in this part are quite general and in fact this part can be considered as a very good textbook on the calssical queueing theory. In the third part some complicated variants of the above classical single channel queue are considered: the bulk queue, priority queues, etc.

The book covers almost all general methods in the theory of single line queueing models. It is of extreme interest for applied mathematicians, computer, electrical and industrial engineers, operations researchers working in queueing theory or using methods and results of the queueing theory.

Reviewer: G. Falin (Moskva)

### MSC:

60K25 | Queueing theory (aspects of probability theory) |

60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |

90B22 | Queues and service in operations research |

00A06 | Mathematics for nonmathematicians (engineering, social sciences, etc.) |