Technical Note—Optimality of Monotonic Policies for Multiple-Server Exponential Queuing Systems with State-Dependent Arrival Rates

Abstract

We consider an exponential queuing system consisting of several removable servers in which the arrival rate depends on the current system state. Costs are incurred at a rate that depends on both the number of customers present and the number of servers in operation. We present conditions that ensure that the number of servers in operation is a non-decreasing function of the number of customers in the system.