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- Title
Stochastic Decomposition in the M/G/1 Queue with Generalized Vacations.
- Authors
Fuhrmann, S. W.; Cooper, Robert B.
- Abstract
This paper considers a class of M/G/1 queueing models with a server who is unavailable for occasional intervals of time. As has been noted by other researchers, for several specific models of this type, the stationary number of customers present in the system at a random point in time is distributed as the sum of two or more independent random variables, one of which is the stationary number of customers present in the standard M/G/1 queue (i.e., the server is always available) at a random point in time. In this paper we demonstrate that this type of decomposition holds, in fact, for a very general class of M/G/1 queueing models. The arguments employed are both direct and intuitive. In the course of this work, moreover, we obtain two new results that can lead to remarkable simplifications when solving complex M/G/1 queueing models.
- Subjects
QUEUING theory; MATHEMATICAL models; MATHEMATICAL decomposition; STATIONARY processes; MATHEMATICAL statistics
- Publication
Operations Research, 1985, Vol 33, Issue 5, p1117
- ISSN
0030-364X
- Publication type
Article
- DOI
10.1287/opre.33.5.1117