Control of service rate for an M/G/1 queue using a short-term cost criterion

A short-term cost criterion is introduced to model the productivity of an M/G/1 queuing/production system; the cost is a weighted sum of penalties associated with the work rate control, penalties associated with part waiting time, and penalties on the increase of parts in the queue, assessed during the time required to serve a single part. The distribution of the service time is of general form, parameterized by the work rate (the control variable). The decision epochs for the optimal control policy are restricted to the times when service is initiated for a part. The major advantages of this formulation are generality and mathematical tractability of the optimal solution. A simple nonlinear search routine is needed to determine the optimal work rate. For the special case of an exponential service time distribution and the special case where service is modeled by a diffusion-threshold process, analytical expressions for the optimal control policy in terms of the queue length are obtained