United Nations Educational Scientific and Cultural Organization INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS OPTIMAL CONTROL OF TWO QUEUES IN SERIES

In this paper we give a fairly complete survey of the available results on the control of arrival and service rates for both single queue and networks of queues. We also study two M/M/l queues in series. At the first queue, the arrival and the service rates are chosen in pair from a finite set whenever the queue lengths at both queues change. Each choice has a switching cost depending on the chosen rates and the queue lengths. At the second queue, the arrival and the service rates are fixed. Our objective is to find a policy for dynamically choosing rates, based on the current rates and queue lengths that minimizes the expected total discounted cost over a finite horizon, numerical results are given.