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Regenerative processes in the theory of queues, with applications to the alternating-priority queue

Published online by Cambridge University Press:  01 July 2016

Shaler Stidham Jr.
Shaler Stidham Jr.*
Affiliation:
Cornell University
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Abstract

Using some well-known and some recently proved asymptotic properties of regenerative processes, we present a new proof in a general regenerative setting of the equivalence of the limiting distributions of a stochastic process at an arbitrary point in time and at the time of an event from an associated Poisson process. From the same asymptotic properties, several conservation equations are derived that hold for a wide class of GI/G/1 priority queues. Finally, focussing our attention on the alternating-priority queue with Poisson arrivals, we use both types of result to give a new, simple derivation of the expected steady-state delay in the queue in each class.

Keywords

QUEUING THEORYPRIORITY QUEUEALTERNATING-PRIORITY QUEUEZERO SWITCH RULEREGENERATIVE PROCESSCUMULATIVE PROCESSCONSERVATION EQUATIONSTIME AVERAGES AND CUSTOMER AVERAGESVIRTUAL AND ACTUAL WAITING TIME
Type
Research Article
Information
Advances in Applied Probability , Volume 4 , Issue 3 , December 1972 , pp. 542 - 577
Copyright
Copyright © Applied Probability Trust 1972 

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