Stochastic control of a queue with two servers of different rates

Abstract

We consider the problem of optimal control of a queueing system consisting of a common queue feeding two servers of different rates. Arrivals to this system form a Poisson process and the service times are exponentially distributed. Whenever a server is idle a decision has to be made on whether to feed a customer from the queue to the idle server. The cost criterion which we desire to minimize is the average number of customers in the system or equivalently, the mean waiting time of the customers. It is shown that the optimal policy is of threshold type, i.e. the slower server should be fed a customer only when the queue length exceeds a certain threshold value.

The research reported in this paper was supported by the U.S. Army Research Office under Contract No. DAAG-29-80-K0038.