On the optimality and the asymptotic optimality of the smallest weighted available buffer policy

Abstract

A major design challenge of Asynchronous Transfer Mode (ATM) networks is to efficiently provide the quality of service (QOS) specified by users with different demands. We classify sources so that sources in one class join the same buffer and have the same requirement for the ATM cell loss ratio. It is important to search for the service discipline that minimizes the accumulated cell loss under the constraint that the cell loss ratios of the sources are proportional to their QOS requirements. In this paper we consider a model that hasNfinite buffers and a single server. Bufferi, of sizeBi, is assigned a positive numberwi. The server serves from one of the non-empty buffers whose indices are equal to argminwi(Bi-Qi), whereQiis the queue length of bufferi. This scheduling policy is called the smallest weighted available buffer policy (SWAB). We show that in a completely symmetric setting, the SWAB policy minimizes the discounted expected loss of cells under some technical conditions. For asymmetric models, we show that the accumulated loss of cells of the SWAB service discipline is asymptotically optimal under heavy traffic conditions in the diffusion limit. Finally, we obtain the expression ofwiso that the cell loss ratios of the sources in the diffusion limit are proportional to their QOS requirements.