Optimal Multiplexing on a

This paper is motivated by the need to provide per session quality of service guarantees in fast packet-switched networks. We address the problem of characterizing and designing scheduling policies that are optimal in the sense of minimizing buuer and/or delay requirements under the assumption of commonly accepted traac constraints. We investigate buuer requirements under three typical memory allocation mechanisms which represent trade-oos between eeciency and complexity. For traac with delay constraints we provide policies that are optimal in the sense of satisfying the constraints if they are satissable by any policy. We also investigate the trade-oo between delay and buuer optimality, and design policies that are \good" (optimal or close to) for both. Finally, we extend our results to the case of \soft" delay constraints and address the issue of designing policies that satisfy such constraints in a fair manner. Given our focus on packet switching , we mainly concern ourselves with non-preemptive policies, but one class of non-preemptive policies which we consider is based on tracking preemptive policies. This class is introduced in this paper and may be of interest in other applications as well.