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Adaptation of the service capacity in a queueing system which is subjected to a change in the arrival rate at unknown epoch

Published online by Cambridge University Press:  01 July 2016

M. Yadin  and
S. Zacks
M. Yadin
Affiliation:
Technion-Israel Institute of Technology
S. Zacks
Affiliation:
Case Western Reserve University
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Abstract

The paper studies the problem of optimal adaptation of an M/M/1 queueing station, when the arrival rate λ0 of customers shifts at unknown epoch, τ, to a known value, λ1. The service intensity of the system starts at μ0 and can be increased at most N times to μ1 < μ2 < · · · < μN. The cost structure consists of the cost changing μi to μj (i + 1 ≦ j ≦ N); of maintaining service at rate μ (per unit of time) and of holding customers at the station (per unit of time). Adaptation policies are constrained by the fact that μ can be only increased. A Bayes solution is derived, under the prior assumption that τ has an exponential distribution. This solution minimizes the total expected discounted cost for the entire future.

Keywords

M/M/1 QUEUEING SYSTEMSADAPTATION OF SERVICE INTENSITYDYNAMIC PROGRAMMINGBAYES ADAPTATIVE POLICY
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 3 , September 1978 , pp. 666 - 681
Copyright
Copyright © Applied Probability Trust 1978 

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References

Crabill, T. B., Gross, D. and Magazine, M. J. (1976) A catalogue of research on optimal design and control of queues. Serial T-341, Program in Logistics, The George Washington University.Google Scholar
Sobel, M. J. (1974) Optimal operation of queues. In Mathematical Methods in Queueing Theory, ed. Clarke, A. B.. Lecture Notes in Economics and Mathematical Systems 98, Springer-Verlag, Berlin, 231–261.CrossRefGoogle Scholar
Stidham, S. Jr. and Prabhu, N. U. (1974) Optimal control of queueing systems. In Mathematical Methods in Queueing Theory, ed. Clarke, A. B.. Lecture Notes in Economics and Mathematical Systems, 98, Springer-Verlag, Berlin, 263–294.CrossRefGoogle Scholar
Yadin, M. (1977) Markovian queueing systems with stochastically varying arrival rates. Technical Report No. 29, ONR Project NR 042–276, Department of Mathematics and Statistics, Case Western Reserve University.Google Scholar
Zacks, S. and Yadin, M. (1970) Analytic characterization of the optimal control of a queueing system. J. Appl. Prob. 7, 617–633.CrossRefGoogle Scholar