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

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Ger Koole ,
Misja Nuyens  and
Rhonda Righter
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: rrighter@ieor.berkeley.edu
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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).

Keywords

Maximum queue lengthbusy periodservice disciplineLCFSvariabilitystochastic orderingbuffer overflow

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Short Communications
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 883 - 891
Copyright
© Applied Probability Trust 2005 

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