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The Effect of Service Time Variability on Maximum Queue Lengths in $M^{X}/G/1$ Queues

Ger Koole, Misja Nuyens and Rhonda Righter
Journal of Applied Probability
Vol. 42, No. 3 (Sep., 2005), pp. 883-891
Stable URL: http://www.jstor.org/stable/30040866
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Effect of Service Time Variability on Maximum Queue Lengths in $M^{X}/G/1$ Queues
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Abstract

We study the impact of service time distributions on the distribution of the maximum queue length during a busy period for the $M^{X}/G/1$ queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite-buffer (M/G/1/n) systems. We show the somewhat surprising result that, for three variations of the preemptive last-come-first-served discipline, the maximum queue length during a busy period is smaller when service times are more variable (in the convex sense).

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