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On the steady-state solution of the M/G/2 queue

Published online by Cambridge University Press:  01 July 2016

Per Hokstad
Per Hokstad*
Affiliation:
University of Trondheim
*
∗Postal address; Institutt for Matematisk Stanistikk, Norges Tekniske H⊘gskole, Universitetet i Trondheim, 7034 Trondheim-NTH, Norway.
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Abstract

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function.

In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.

Keywords

M/G/2 QUEUEQUEUE LENGTH
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 1 , March 1979 , pp. 240 - 255
Copyright
Copyright © Applied Probability Trust 1979 

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