Delay Optimal Transmission Policy in a Wireless Multiaccess Channel

In this correspondence, we consider the problem of delay optimal rate allocation in a (potentially asymmetric) multiaccess channel. The rate feasibility region of such a network is well studied and is shown to be of a polymatroid structure. 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 correspondence, 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.