End-to-end delay bounds for traffic aggregates under guaranteed-rate scheduling algorithms

This paper evaluates, via both analysis and simulation, the end-to-end (e2e) delay performance of aggregate scheduling with guaranteed-rate (GR) algorithms. Deterministic e2e delay bounds for a single aggregation are derived under the assumption that all incoming flows at an aggregator conform to the token bucket model. An aggregator can use any of three types of GR scheduling algorithms: stand-alone GR, two-level hierarchical GR, and rate-controlled two-level hierarchical GR. E2e delay bounds are also derived for the case of multiple aggregations within an aggregation region when aggregators use the rate-controlled two-level hierarchical GR. By using the GR scheduling algorithms for traffic aggregates, we show not only the existence of delay bounds for each flow, but also the fact that, under certain conditions (e.g., when the aggregate traverses a long path after the aggregation point), the bounds are smaller than that of per-flow scheduling. We then compare the analytic delay bounds numerically and conduct in-depth simulation to: 1) confirm the analytic results and 2) compare the e2e delays of aggregate and per-flow scheduling. The simulation results have shown that aggregate scheduling is very robust and can exploit statistical multiplexing gains. It performs better than per-flow scheduling in most of the simulation scenarios we considered. Overall, aggregate scheduling is shown theoretically to provide bounded e2e delays and practically to provide excellent e2e delay performance. Moreover, it incurs lower scheduling and state-maintenance overheads at routers than per-flow scheduling. All of these salient features make aggregate scheduling very attractive for use in Internet core networks.