Service Control in a Finite Buffered Queue with Multiple Service Rates

We consider a finite buffered queue in which the queue length is controlled by dynamically selecting between two possible service rates (low and high). Using the faster service rate requires higher operating costs which may justify using the slower rate from time to time. Moreover, the system incurs holding costs for customers waiting to be processed and setup costs for each service rate change. When both service rates are close to the arrival rate, a heavy traffic (diffusion) approximation is valid for the expected queue length for this system. Furthermore, the approximating dynamic control problem has an explicit solution for a special case of the parameters which leads to an approximate solution for the general case. We present numerical examples that analyze the validity of the heavy traffic approach.