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Some general results for many server queues

Published online by Cambridge University Press:  01 July 2016

J. H. A. De Smit
J. H. A. De Smit*
Affiliation:
Center for Operations Research and Econometrics, University of Louvain
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Abstract

Pollaczek's theory for the many server queue is generalized and extended. Pollaczek (1961) found the distribution of the actual waiting times in the model G/G/s as a solution of a set of integral equations. We give a somewhat more general set of integral equations from which the joint distribution of the actual waiting time and some other random variables may be found. With this joint distribution we can obtain distributions of a number of characteristic quantities, such as the virtual waiting time, the queue length, the number of busy servers, the busy period and the busy cycle. For a wide class of many server queues the formal expressions may lead to explicit results.

Keywords

MANY SERVER QUEUEPOLLACZEK'S METHODANALYTIC METHODACTUAL WAITING TIMEVIRTUAL WAITING TIMEBUSY CYCLEBUSY PERIODQUEUE LENGTHOUTPUT PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 1 , April 1973 , pp. 153 - 169
Copyright
Copyright © Applied Probability Trust 1973 

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