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Queues with random service output: the case of Poisson arrivals

Published online by Cambridge University Press:  14 July 2016

Jacob Grinstein  and
Michael Rubinovitch
Jacob Grinstein
Affiliation:
Technion — Israel Institute of Technology
Michael Rubinovitch
Affiliation:
Technion — Israel Institute of Technology
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Abstract

A general class of single server queueing models is formulated. They distinguish between two factors that may influence the duration of service times: variability in the service requirements of customers, and variability (over time) in the service output of the server. Accordingly, we assume that the demands for service of successive customers form a sequence of independent, identically distributed random variables and that the amount of service produced by a busy server in a time interval is determined by the increment of a process with stationary independent increments over that interval. The results include the distribution of the busy period and the limiting distribution of the queue length. We also investigate the potential waiting process which is an extension of virtual waiting time process in existing queueing models.

Keywords

QUEUEING THEORYPROCESSES WITH STATIONARY INDEPENDENT INCREMENTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 771 - 784
Copyright
Copyright © Applied Probability Trust 1974 

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