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The effect of service time variability on maximum queue lengths in MX/G/1 queues

Published online by Cambridge University Press:  14 July 2016

Ger Koole*
Affiliation:
Vrije Universiteit Amsterdam
Misja Nuyens*
Affiliation:
Vrije Universiteit Amsterdam
Rhonda Righter*
Affiliation:
University of California, Berkeley
*
Postal address: Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands.
Postal address: Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands.
∗∗∗∗Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA. Email address: [email protected]
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Abstract

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We study the impact of service time distributions on the distribution of the maximum queue length during a busy period for the MX/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).

MSC classification

Type
Short Communications
Copyright
© Applied Probability Trust 2005 

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