Providing End-to-End Statistical Delay Guarantees with Earliest Deadline First Scheduling and Per-Hop Traffic Shaping

This paper develops a framework for statistically guaranteeing end-to-end delay bounds to leaky-bucket-constrained flows transporting real-time traffic in a network of switches using Earliest Deadline First (EDF) packet scheduling and per-hop traffic shaping. We first analyze the delay-bound violation probabilities at an isolated EDF scheduler fed by fluid source processes generating extremal dual-leaky-bucket-regulated traffic. We compute a close upper bound by applying the Beneš approach to an equivalent hypothetical system derived from the real one. We then extend the analysis to the end-to-end scenario in presence of traffic reshaping at each node in the network. We compare the analytical results with simulations, and show that the match is very close. We also investigate the advantages of smoothing the traffic at the ingress to the network, and propose a simple choice of smoothing parameters, which performs very well. Using realistic traffic parameters, we compare the schedulable region of our statistical framework with that of the corresponding deterministic framework, and demonstrate that the statistical framework allows tremendous improvements in network utilization, even for very low delay-violation probabilities. The framework developed in this paper is therefore highly useful in practical packet networks to provide quality of service to real-time applications in the form of statistical, rather than deterministic, end-to-end delay bounds. Keywords— Scheduling, Earliest Deadline First, Statistical Delay Bounds, Schedulable Region.