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**Queueing systems with vacations - a survey.**
*(English)*
Zbl 0655.60089

In this excellent review article single-server queueing models with vacations are discussed. The author aims at (and succeeds in) providing a methodological overview with the objective to illustrate how the seemingly diverse mix of problems where vacation models arise in some form is closely related in structure and can be understood in a common framework.

After describing a large number of problems which can be addressed by vacation-type models, the author selects two models for detailed treatment. For these models, which are generalizations of the standard GI/G/1 queue, a variety of techniques used (to obtain decomposition results, in particular) and the scope and limitations of each is discussed. It is then shown how understanding the behaviour of these two models helps to analyse other vacation models using similar techniques. Some applications and a discussion of some unsolved problems conclude the paper.

After describing a large number of problems which can be addressed by vacation-type models, the author selects two models for detailed treatment. For these models, which are generalizations of the standard GI/G/1 queue, a variety of techniques used (to obtain decomposition results, in particular) and the scope and limitations of each is discussed. It is then shown how understanding the behaviour of these two models helps to analyse other vacation models using similar techniques. Some applications and a discussion of some unsolved problems conclude the paper.

Reviewer: E.A.van Doorn

### MSC:

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

90B22 | Queues and service in operations research |

Full Text:
DOI

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