Traffic shaping for end-to-end delay guarantees with EDF scheduling

The provision of quality of service (QoS) in terms of end-to-end delay guarantees to real-time applications is an important issue in emerging broadband packet networks. Of the various packet scheduling schemes that have been proposed in the literature, earliest deadline first (EDF) scheduling in conjunction with per-hop traffic shaping (jointly referred to as rate-controlled EDF or RC-EDF) has been recognized as an effective means of end-to-end deterministic delay provisioning. An important aspect that has not been addressed satisfactorily in the literature, however, concerns the choice of RC-EDF shaping parameters that realize maximal network utilizations. In this paper, we first establish that except in trivial cases, it is infeasible to identify "optimal" shapers that realize maximal RC-EDF schedulable regions. Ascertaining the optimal flow shaper requires the state of the entire network to be considered, making it computationally impractical. We then propose an heuristic choice of shaper derived from the number of hops traversed by the flow. The resulting shaper is easy to compute, and varies gracefully between the known optimal shapers for limiting values of the hop-length. We show via simulations that for a realistic traffic mix, our choice of shaper allows RC-EDF to outperform the GPS (generalized processor sharing) scheduling discipline as well as RC-EDF disciplines that use shapers chosen independent of the flow hop-length.