Asymptotically Optimal Admission Control of a Queue with Impatient Customers

Authors:
Amy R. Ward;Sunil Kumar
Affiliations:
Marshall School of Business, USC, Los Angeles, California 90089-0809;Graduate School of Business, Stanford University, Stanford, California 94705-5015
Venue:
Mathematics of Operations Research
Year:
2008

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Abstract

We consider a GI/GI/1 queue with impatient customers in heavy traffic. We use the solution of an approximating singular diffusion control problem to construct an admission control policy for the queue. The approximating control problem does not admit a so-called pathwise solution. Hence, the resulting admission control policy depends on second-moment data. We prove asymptotic optimality of the constructed policy using weak-convergence methods.rh