Abstract

In this paper we consider the problem of optimal rate allocation in a (potentially asymmetric) multi-access channel. The rate feasibility region of such a network is well-studied. In other words, it is known that for the case of saturated sources any point on the boundary maximizes the throughput. We consider this problem with unsaturated sources, i.e. jobs arrive at sources at random times and the source has the possibility of being empty. In such a setting, all stable rate allocation policies result in a throughput matched with the average arrival rate. Hence, we are interested in rate allocation policies that minimize expected delay in the system. In this paper, we show that a policy of threshold type is optimal in minimizing the average queueing delay. We study the average delay criterion as the limit of an infinite horizon discounted cost function when the discount factor approaches 1. I.

Citations