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The G/M/m queue with finite waiting room

Published online by Cambridge University Press:  14 July 2016

Per Hokstad
Per Hokstad*
Affiliation:
University of Trondheim
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Abstract

The G/M/m queue with only s waiting places is studied. We start by studying the joint distribution of the number of customers present at time t and the time elapsing until the next arrival after t. This gives the asymptotic distribution of the number of customers at the moment of an arrival and at an arbitrary moment. Then waiting time and virtual waiting time distributions are easily obtained. For the G/M/1 queue also the transient solution is given. Finally the case s = ∞ is considered.

Keywords

G/M/m QUEUEFINITE WAITING ROOMNUMBER OF CUSTOMERSWAITING TIMETRANSIENT SOLUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 779 - 792
Copyright
Copyright © Applied Probability Trust 1975 

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References

Cohen, J. W. (1969) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
Smit, J. H. A. De (1973) On the many server queue with exponential service times. Adv. Appl. Prob. 5, 170–182.Google Scholar
Hokstad, P. (1975a) A supplementary variable technique applied to the M/G/1 queue. Scand. J. Statist. 2.Google Scholar
Hokstad, P. (1975b) The use of Wiener-Hopf decomposition in the study of waiting time and busy period for the G/G/1 queue. Scand. J. Statist. To appear.Google Scholar
Keilson, J. (1966) The ergodic queue length distribution for queueing systems with finite capacity. J. Roy. Statist. Soc. B 28, 190–201.Google Scholar
Takács, L. (1958) On a combined waiting time and loss problem concerning telephone traffic. Mathematical Institute, Loránd Eötvös University, Budapest, 73–82.Google Scholar
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
Schassberger, R. (1970) On the waiting time in the queueing system G/G/1. Ann. Math. Statist. 41, 182–187.Google Scholar