Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations

S. W. Fuhrmann and Robert B. Cooper
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S. W. Fuhrmann: AT&T Bell Laboratories, Holmdel, New Jersey
Robert B. Cooper: Florida Atlantic University, Boca Raton, Florida

Operations Research, 1985, vol. 33, issue 5, 1117-1129

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.

Keywords: 681 queues; 691 feedback (search for similar items in EconPapers)
Date: 1985
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Citations: View citations in EconPapers (57)

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