QPS-r: A Cost-Effective Crossbar Scheduling Algorithm and Its Stability and Delay Analysis
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Parallel iterative maximal matching algorithms (adapted for switching) has long been recognized as a cost-effective family for crossbar scheduling. On one hand, they provide the following Quality of Service (QoS) guarantees: Using maximal matchings as crossbar schedules results in at least 50 throughput and order-optimal (i.e., independent of the switch size N) average delay bounds for various traffic arrival processes. On the other hand, using N processors (one per port), their per-port computational complexity can be as low as O(^2 N) (more precisely O( N) iterations that each has O( N) computational complexity) for an N× N switch. In this work, we propose QPS-r, a parallel iterative switching algorithm that has the lowest possible computational complexity: O(1) per port. Yet, the matchings that QPS-r computes have the same quality as maximal matchings in the following sense: Using such matchings as crossbar schedules results in exactly the same aforementioned provable throughput and delay guarantees as using maximal matchings, as we show using Lyapunov stability analysis. Although QPS-r builds upon an existing add-on technique called Queue-Proportional Sampling (QPS), we are the first to discover and prove this nice property of such matchings. We also demonstrate that QPS-3 (running 3 iterations) has comparable empirical throughput and delay performances as iSLIP (running _2 N iterations), a refined and optimized representative maximal matching algorithm adapted for switching.
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