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Analytical solution of finite capacity M/D/1 queues

Part of: Special processes Computer system organization

Published online by Cambridge University Press:  14 July 2016

Olivier Brun  and
Jean-Marie Garcia
Olivier Brun*
Affiliation:
LAAS-CNRS
Jean-Marie Garcia*
Affiliation:
LAAS-CNRS
*
∗ Postal address: Laboratoire d'Analyse et d'Architecture des Systèmes du CNRS, Toulouse, France.
∗ Postal address: Laboratoire d'Analyse et d'Architecture des Systèmes du CNRS, Toulouse, France.
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Abstract

Although the M/D/1/N queueing model is well solved from a computational point of view, there is no known analytical expression of the queue length distribution. In this paper, we derive closed-form formulae for the distribution of the number of customers in the system in the finite-capacity M/D/1 queue. We also give an explicit solution for the mean queue length and the average waiting time.

Keywords

Finite capacity M/D/1 queuesembedded Markov chainqueue length distributionmean number of customersaverage waiting time

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1092 - 1098
Copyright
Copyright © by the Applied Probability Trust 2000 

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References

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