Abstract
This paper deals with the problem of controlling an exponential queuing system (that is, a system with exponential service times and Poisson arrivals) so as to stochastically minimize the number of customers in the system at any time t > 0. Sufficient (simple) conditions are developed for a policy to be optimal. Similar conditions are sufficient for a policy to stochastically minimize (maximize) any function of the state of the system. Two models are considered to illustrate the results. In both cases, optimal policies are shown to satisfy these conditions by a simple inductive procedure.
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