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On the many server queue with exponential service times

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

The general theory for the many server queue due to Pollaczek (1961) and generalized by the author (de Smit (1973)) is applied to the system with exponential service times. In this way many explicit results are obtained for the distributions of characteristic quantities, such as the actual waiting time, the virtual waiting time, the queue length, the number of busy servers, the busy period and the busy cycle. Most of these results are new, even for the special case of Poisson arrivals.

Keywords

MANY SERVER QUEUEPOLLACZEK'S METHODEXPONENTIAL SERVICE TIMESACTUAL WAITING TIMEVIRTUAL WAITING TIMEBUSY CYCLEBUSY PERIODQUEUE LENGTH, OUTPUT PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 1 , April 1973 , pp. 170 - 182
Copyright
Copyright © Applied Probability Trust 1973 

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References

Bhat, U. N. (1966) The queue GI/M/2 with service rate depending on the number of busy servers. Ann. Inst. Statist. Math. 18, 211–221.CrossRefGoogle Scholar
Cohen, J. W. (1969) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
De Smit, J. H. A. (1971) Many Server Queueing Systems. Ph. D. dissertation, University of Technology, Delft.Google Scholar
De Smit, J. H. A. (1973) Some general results for many server queues. Adv. Appl. Prob. 5, 153–169.CrossRefGoogle Scholar
Kendall, D. G. (1953) Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. Ann. Math. Statist. 24, 338–354.CrossRefGoogle Scholar
Pollaczek, F. (1953) Sur une généralisation de la théorie des attentes. C. R. Acad. Sci. Paris, 236, 578–580.Google Scholar
Pollaczek, F. (1961) Théorie Analytique des Problèmes Stochastiques Relatifs à un Groupede Lignes Téléphoniques avec Dispositif d'Attente. Gauthier-Villars, Paris.Google Scholar
Takács, L. (1957) On a queueing problem concerning telephone traffic. Acta. Math. Acad. Sci. Hungar. 8, 325–335.CrossRefGoogle Scholar