Work-Conserving Distributed Schedulers

Buffered multistage interconnection networks offer one of the most scalable and cost-effective approaches to building high capacity routers and switches. Unfortunately, the performance of such systems has been difficult to predict in the presence of the extreme traffic conditions that can arise in Internet routers. Recent work introduced the idea of distributed scheduling, to regulate the flow of traffic in such systems. This work demonstrated (using simulation and experimental measurements) that distributed scheduling can enable robust performance, even in the presence of adversarial traffic patterns. In this paper, we show that appropriately designed distributed scheduling algorithms are provably work-conserving for speedups of 2 or more. Two of the three algorithms presented were inspired by algorithms previously developed for crossbar scheduling. The third has no direct counterpart in the crossbar scheduling context. In our analysis, we show that distributed schedulers based on blocking flows in small-depth acyclic flow graphs can be workconserving, just as certain crossbar schedulers based on maximal bipartite matchings have been shown to be work-conserving. We also study the performance of practical variants of the work-conserving algorithms with speedups less than 2, using simulation. These studies demonstrate that distributed scheduling ensures excellent performance under extreme traffic conditions for speedups of less than 1.5. This work was supported by the Defense Advanced Research Projects Agency (contract N660001-01-1-8930).