QPS-r

Abstract

In an input-queued switch, a crossbar schedule, or a matching between the input ports and the output ports needs to be computed for each switching cycle, or time slot. It is a challenging research problem to design switching algorithms that produce high-quality matchings yet have a very low computational complexity when the switch has a large number of ports. Indeed, there appears to be a fundamental tradeoff between the computational complexity of the switching algorithm and the quality of the computed matchings.Parallel maximal matching algorithms (adapted for switching) appear to be a sweet tradeoff point in this regard. On one hand, they provide the following performance guarantees: Using maximal matchings as crossbar schedules results in at least 50% switch throughput and order-optimal (i.e., independent of the switch size N) average delay bounds for various traffic arrival processes. On the other hand, their computational complexities can be as low as O(log2 N) per port/processor, which is much lower than those of the algorithms for finding matchings of higher qualities such as maximum weighted matching.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 log2 N iterations), a refined and optimized representative maximal matching algorithm adapted for switching.