Access control of parallel multiserver loss queues

This paper considers access control in a target multiserver loss queue fed by a set of upstream parallel multiserver loss queues and by a stream of new customers. The target queue faces a choice of how many servers to reserve for each stream. Revenue is gained by each station when it serves a customer, but the amount of revenue at the target queue depends on the source of the customer. We prove that the policy that maximizes total discounted revenue consists of a set of monotonically decreasing thresholds as functions of the occupancy of each queue. We prove monotonicity properties with respect to system parameters. We show that there exists an ordering of the thresholds based on the relative revenue paid at the target queue. Finally, we compare this system with a tandem queue model.