We consider admission policies to two multiserver loss queues in series with two types of traffic. Both are generated according to independent Poisson processes with constant arrival rates. The first type requires service at the first queue and with a positive probability enters the second queue; the second type requires service at only the second queue. The service time distribution is exponential at either station. We show that under appropriate conditions the optimal admission policy that maximizes the expected total discounted reward over an infinite horizon is given by a switching curve. We characterize the form and shape of this curve and its variation with system parameters.

This paper considers access control policies in multiserver loss queues in series such as might arise in the context of computer and telecommunication networks. Each queue is presented with both served upstream customers and Poisson arrivals from outside the network, and it may route serviced customers out of the network or to the downstream queue. Service times of each customer are i.i.d. and exponentially distributed. Revenue is earned by each station when it serves a customer, but the amount of revenue depends on whether the customer entered the network at this station or was routed from an upstream station. We propose a simple recursive method to solve the problem using dynamic programming on a set of reduced state spaces. This approach includes a rate estimation technique for upstream stations, and a revenue estimation technique for downstream stations. Numerical results demonstrate the performance of these near-optimal policies under light, moderate, and heavy traffic.

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.