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Transient analytical solution of M/D/1/N queues

Part of:Special processesComputer system organization

Published online by Cambridge University Press:  14 July 2016

Jean-Marie Garcia,
Olivier Brun and
David Gauchard
Jean-Marie Garcia*
Affiliation:
LAAS-CNRS
Olivier Brun*
Affiliation:
LAAS-CNRS
David Gauchard*
Affiliation:
LAAS-CNRS
*
∗ Postal address: Laboratoire d’Analyse et d’Architecture des Systèmes du CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cedex 4, France.
∗ Postal address: Laboratoire d’Analyse et d’Architecture des Systèmes du CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cedex 4, France.
∗ Postal address: Laboratoire d’Analyse et d’Architecture des Systèmes du CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cedex 4, France.
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Abstract

An analytical expression of the time-dependent probability distribution of M/D/1/N queues initialised in an arbitrary deterministic state is derived. We also obtain a simple analytical expression of the differential equation governing the transient average traffic which only involves probabilities of boundary states. As a by-product, a closed form solution of the departure rate from the system is also determined.

Keywords

Finite capacity M/D/1 queuestransient probability distribution

MSC classification

Primary:60K25: Queueing theory
Secondary:68M20: Performance evaluation; queueing; scheduling

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002, pp. 853 - 864
Copyright
Copyright © Applied Probability Trust 2002 

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