Busy Period Control of Queues Based on Waiting Times at Arrivals

System maintenance and vehicular traffic control problems have motivated the queue control systems studied here. This article presents results for optimal assignment of servers or rejection of customers, on the basis of arriving customers' waiting times w_n, when the objective function is the mean of a control penalty plus a variable such as busy period duration, number served in a busy period, or total delay to all customers in a busy period. Under the first two criteria, we generalize previous results for M/M/1 queues to similar results for the M/G/1 case. We show that the optimal customer rejection (vehicle diversion) to minimize total delay to accepted and rejected (detoured) customers is of the control-limit form for the M/G/1 case and give an explicit expression for the optimal threshold for the M/M/1 case.