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The mean waiting time in a G/G/m/∞ queue with the LCFS-P service discipline

Published online by Cambridge University Press:  01 July 2016

Gunter Ritter  and
Ulrich Wacker
Gunter Ritter
Affiliation:
Universität Passau
Ulrich Wacker*
Affiliation:
Universität Passau
*
∗Postal address: Fakultät für Mathematik und Informatik der Universität, D-W8390 Passau, Germany.
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Abstract

A single- or multiserver queue with work-conserving service discipline and a stationary and ergodic input stream with bounded service times and arbitrarily light traffic intensity may have infinite mean waiting time. We give an example of this paradox and we also give a mixing condition which, in the case of the preemptive-resume LCFS discipline, excludes this phenomenon. Furthermore, the same methods allow to estimate the durations of the first busy period and cycle and the number of customers served in the first busy cycle of a work-conserving queue.

Keywords

PREEMPTIVE-RESUME LCFSWORK CONSERVINGSTATIONARY AND ERGODIC INTERARRIVAL AND SERVICE TIMESMIXING CONDITIONBUSY CYCLEBUSY PERIOD
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 2 , June 1991 , pp. 406 - 428
Copyright
Copyright © Applied Probability Trust 1991 

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