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Optimal Control of Arrivals to Queues with Delayed Queue Length Information

Kuri, Joy and Kumar, Anurag (1992) Optimal Control of Arrivals to Queues with Delayed Queue Length Information. In: 31st IEEE Conference on Decision and Control, 1992, 16-18 December, Tucson,Artzona, vol.1, 997 -998.

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Abstract

We consider discrete time versions of two classical problems in the optimal control of admission to a queueing system:(i) optimal routing of arrivals to two parallel queues and (ii) optimal acceptance/rejection of arrivals to a single queue. We extend the formulation of these problems to permit a k step delay in the observation of the queue lengths by the controller. For geometric inter-arrival times and geometric service times the problems are formulated as Controlled Markov Chains with expected total discounted cost as the minimization objective. For problem (i) we show that when k = 1, the optimal policy is to allocate an arrival to the queue with the smaller expected queue length (JSEQ: Join the Shortest Expected Queue) For $k\geq2$, however, JSEQ is not optimal. For problem (ii) we show that when k = 1, the optimal policy is a threshold policy. There are, however, two thresholds $m_0\geq$$m_l>0$, such that $m_0$ is used when the previous action was to reject, and $m_1$ is used when the previous action was to accept.

Item Type: Conference Paper
Additional Information: Copyright 1990 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 27 May 2006
Last Modified: 19 Sep 2010 04:27
URI: http://eprints.iisc.ernet.in/id/eprint/7004

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