Optimal allocation of priority in a M/M/1 queue with two types of customers

摘要

We consider a M/M/1 queue with two types of customers.The server suffers some loss when a non-priority customer joins the queue if the size of the queue is greater than some predetermined level N. The problem is to decide which group receives priority in such a way as to minimize the expected cost per unit of time.We show first how to determine the optimal decision. Then we introduce approximations that enable us to show that the optimal decision has a simple behaviour as a function of N, the arrival and service parameters.