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Discrete queues with one server

Published online by Cambridge University Press:  14 July 2016

Lajos Takács
Lajos Takács*
Affiliation:
Case Western Reserve University
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Extract

In this paper mathematical methods are given for finding the distributions of the virtual waiting time and the occupation time for single-server queues in which the interarrival times and the service times are discrete random variables taking on positive or non-negative integral values. First we shall consider deterministic queues in which the interarrival times and the service times are numerical (non-random) quantities and deduce a fundamental relation for such queues. Then we shall consider random queues with recurrent input and general service times and study the time dependent behavior of such queues.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 691 - 707
Copyright
Copyright © Applied Probability Trust 1971 

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