Exponential Penalty Function Control of Loss Networks

We introduce penalty-function-based admission control policies to approximately maximize the expected reward rate in a loss network. These control policies are easy to implement and perform well both in the transient period as well as in steady state. A major advantage of the penalty approach is that it avoids solving the associated dynamic program. However, a disadvantage of this approach is that it requires the capacity requested by individual requests to be sufficiently small compared to total available capacity. We first solve a related deterministic linear program (LP) and then translate an optimal solution of the LP into an admission control policy for the loss network via an exponential penalty function. We show that the penalty policy is a target-tracking policy—it performs well because the optimal solution of the LP is a good target. We demonstrate that the penalty approach can be extended to track arbitrarily defined target sets. Results from preliminary simulation studies are included. 1. Introduction. We consider the following dynamic stochastic allocation problem (details in Section 2). The stochastic system consists of a network of resources (facilities), each with a known fixed capacity. Requests for using this network belong to a diverse set of request classes, differing in the arrival rate, the service duration, the resource requirements and the willingness to pay. There is no waiting room (queue), therefore an arriving request must be either admitted into the system for service and assigned an appropriate resource allocation or rejected (lost) at the instant it arrives. An admitted request occupies the allocated resources for the service duration and releases all the resources simultaneously. The objective of the