Optimal Admission Control In Queues With Workload-Dependent Service Rates

Authors:
René Bekker;Sem C. Borst
Affiliations:
Vrije Universiteit, Amsterdam, 1081 HV Amsterdam, The Netherlands, E-mail: rbekker@few.vu.nl;Department of Mathematics & Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, and, CWI, 1090 GB Amsterdam, The Netherlands, and, Bell Laboratories, Lucent T ...
Venue:
Probability in the Engineering and Informational Sciences
Year:
2006

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Abstract

We consider a queuing system with a workload-dependent service rate. We specifically assume that the service rate is first increasing and then decreasing as a function of the amount of work. The latter qualitative behavior is quite common in practical situations, such as production systems. The admission of work into the system is controlled by a policy for accepting or rejecting jobs, depending on the state of the system. We seek an admission control policy that maximizes the long-run throughput. Under certain conditions, we show that a threshold policy is optimal, and we derive a criterion for determining the optimal threshold value.