On the optimal switching level for an M/G/1 queueing system

AbstractA cost function is studied for an M/G/1 queueing model for which the service rate of the virtual waiting time process Ut for Ut<K differs from that for Ut > K. The costs considered are costs for maintaining the service rate, costs for switching the service rate and costs proportional to the inventory Ut. The relevant cost factors for the system operating below level K differ from those when Ut > K. The cost function which is considered only for the stationary situation of the Ut-process expresses the average cost per unit time. The problem is to find that K for which the cost function reaches a minimum. Criteria for the possibly optimal cases are found; they have an interesting intuitive interpretation, and require the knowledge of only the first moment of the service time distribution