Optimal Pricing for Finite Capacity Queueing Systems with Multiple Customer Classes

We determine optimal static prices for a finite capacity queueing system serving customers from different classes. We prove an upper bound for the optimal arrival rates for a fairly large class of queueing systems and provide sufficient conditions that ensure the existence of a unique optimal arrival rate vector. We show that these conditions hold for M/M/1/m and M/G/s/s systems and prove structural results on the relationships between the optimal arrival rates and system capacity. We also prove structural results on the optimal prices and provide conditions that ensure that the optimal price for one of the customer classes is higher than the optimal price for another class. Finally, we test the generality of some of our theoretical results by a numerical study.