Scheduling arrivals to queues

An algorithm is developed to determine the schedule for n arrivals to a single server exponential first come, first served service which will minimize the sum of customer waiting and server availability costs. The algorithm results in an n − 1 dimensional objective function which has been shown to be convex for n ⩽ 4 and is suspected to be convex for n ⩾ 5. The difficulty in demonstrating convexity for n ⩾ 5 is indicated.