A General Methodology for Designing Eecient Traac Scheduling and Shaping Algorithms

We introduce a general methodology for designing integrated shaping and scheduling algorithms for packet networks that provide fairness, low end-to-end delay, and low burstiness. The methodology is based on integrating a shaping mechanism with a scheduler from the class of Rate-Proportional Servers (RPS) deened in 10]. The resulting algorithms provide an end-to-end delay bound identical to that of Weighted Fair Queueing. Their worst-case fairness, in terms of minimizing the worst-case delay to empty the session backlog, is much superior to that of Weighted Fair Queueing, and equal to the best known for any scheduling algorithm. In addition, the algorithms achieve a level of fairness in the distribution of free bandwidth among competing sessions better than that of Weighted Fair Queue-ing. We show that, under this framework, even an unfair scheduling algorithm belonging to the RPS class, such as VirtualClock, can yield worst-case fairness identical to that obtained with Weighted Fair Queueing. We also develop an integrated shaper-scheduler that provides optimal output burstiness and is attractive for use in both network adapters and in switches that support traac reshaping. We describe an eecient implementation of this integrated shaping and scheduling algorithm with log 2 (V) complexity, where V is the number of sessions sharing the outgoing link.