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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

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