Some properties of optimal control policies for entry to an M/M/1 queue

Customers served by an M/M/1 queueing system each receive a reward R but pay a holding cost of C per unit time (including service time) spent in the system. The decision of whether or not a customer joins the queue can be made on an individual basis or a social basis. The effect of increasing the arrival rate on the optimal policy parameters is examined. Some limiting results are also derived.