Dynamic Control of a Queue with Adjustable Service Rate

Jennifer M. George () and J. Michael Harrison ()
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Jennifer M. George: Melbourne Business School, 200 Leicester St, Carlton, Victoria 3053, Australia
J. Michael Harrison: Graduate School of Business, Stanford University, Stanford, California 94305

Operations Research, 2001, vol. 49, issue 5, 720-731

Abstract: We consider a single-server queue with Poisson arrivals, where holding costs are continuously incurred as a nondecreasing function of the queue length. The queue length evolves as a birth-and-death process with constant arrival rate (lambda) = 1 and with state-dependent service rates (mu) n that can be chosen from a fixed subset A of [0, (infinity)). Finally, there is a nondecreasing cost-of-effort function c (·) on A, and service costs are incurred at rate c ((mu) n ) when the queue length is n . The objective is to minimize average cost per time unit over an infinite planning horizon. The standard optimality equation of average-cost dynamic programming allows one to write out the optimal service rates in terms of the minimum achievable average cost (zeta)*. Here we present a method for computing (zeta)* that is so fast and so transparent it may be reasonably described as an explicit solution for the problem of service rate control. The optimal service rates are nondecreasing as a function of queue length and are bounded if the holding cost function is bounded. From a managerial standpoint it is natural to compare (zeta)*, the minimum average cost achievable with state-dependent service rates, against the minimum average cost achievable with a single fixed service rate. The difference between those two minima represents the economic value of a responsive service mechanism, and numerical examples are presented that show it can be substantial.

Keywords: Queues: dynamic control; Dynamic programming: service rate control in queues (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (44)

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