Near optimal admission control for multiserver loss queues in series

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.