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Computation of the stationary distribution of the queue size in an M/G/1 queueing system with variable service rate

Published online by Cambridge University Press:  14 July 2016

A. Federgruen  and
H. C. Tijms
A. Federgruen
Affiliation:
Mathematisch Centrum, Amsterdam
H. C. Tijms*
Affiliation:
Vrije Universiteit, Amsterdam
*
∗∗Postal address: Vrije Universiteit, Interfakulteit Actuariële Wetenschappen en Econometrie, de Boelelaan 1081, Postbus 7161, 1007 MC Amsterdam, The Netherlands.
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Abstract

This paper presents a simple and computationally tractable method which recursively computes the stationary probabilities of the queue size in an M/G/1 queueing system with variable service rate. For each service two possible service types are available and the service rule is characterized by two switch-over levels. The computational approach discussed in this paper can be applied to a variety of queueing problems.

Keywords

M/G/1 QUEUEING SYSTEMVARIABLE SERVICE RATESWITCH-OVER SERVICE RULEQUEUE SIZESTATIONARY DISTRIBUTIONCOMPUTATIONAL METHOD
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 515 - 522
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

∗

Present address: Graduate School of Business, Columbia University, Uris Hall, New York, NY 10027, U.S.A.

References

Cooper, R. B. (1972) Introduction to Queueing Theory. MacMillan, New York.Google Scholar
Gavish, B. (1978) A direct method for computing stationary state probabilities for M/G/1 queues with setup times and group arrivals. Working Paper Series Number 7828, Graduate School of Management, University of Rochester.Google Scholar
Hordijk, A. and Tijms, H. C. (1976) A simple proof of the equivalence of the limiting distributions of the continuous-time and the embedded process of the queue size in the M/G/1 queue. Statist. Neelandica 30, 97–100.CrossRefGoogle Scholar
Keilson, J. (1966) The ergodic queue length distribution for queueing systems with finite capacity. J. R. Statist. Soc. B 28, 190–201.Google Scholar
Levy, Y. and Yechiali, U. (1975) Utilization of idle time in an M/G/1 queueing system. Management Sci. 22, 202–211.Google Scholar
Loris-Teghem, J. (1978) Hysteric control of an M/G/1 queueing system with two service time distributions and removable server. University of Mons, Belgium.Google Scholar
Neuts, M. F. (1977) Algorithms for waiting time distributions under various queue disciplines in the M/G/1 queue with service time distributions of the phase type. In Algorithmic Methods in Probability, ed. Neuts, M. F., North-Holland, Amsterdam, 177–197.Google Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
Stidham, S. Jr. (1972) Regenerative processes in the theory of queues with applications to the alternating priority queue. Adv. Appl. Prob. 4, 542–577.Google Scholar
Tijms, H. C. (1978) An algorithm for average costs denumerable state semi-Markov decision problems with applications to controlled production and queueing systems. In Recent Developments in Markov Decision Theory, ed. White, D. J., Academic Press, New York.Google Scholar