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Optimal Server Allocation to Parallel Queues with Finite-Capacity Buffers

Published online by Cambridge University Press:  27 July 2009

K. M. Wasserman  and
Nicholas Bambos
K. M. Wasserman
Affiliation:
Department of Electrical Engineering, University of California at Los Angeles Los Angeles, California 90024
Nicholas Bambos
Affiliation:
Department of Electrical Engineering, University of California at Los Angeles Los Angeles, California 90024
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Extract

In this paper, we study the problem of dynamic allocation of a single server to parallel queues with finite-capacity buffers. The arrival processes are mutually independent, equal rate Poisson processes, and the service times are independent and identically distributed random variables with an arbitrary distribution. We are interested in characterizing the allocation policy that stochastically minimizes the number of customers lost due to buffer overflows. Using a coupling argument, we establish the optimality of the Fewest-Empty-Spaces policy, which allocates the server to the queue with the fewest empty buffer spaces, within the class of nonpreemptive and nonidling policies. The result extends to the class of preemptive policies, if the service times are exponentially distributed. We also briefly discuss the allocation problem under more general statistical assumptions on the arrival processes.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 2 , April 1996 , pp. 279 - 285
Copyright
Copyright © Cambridge University Press 1996

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