On the throughput achievable by isolated and interconnected input-queueing switches under multiclass traffic

Many studies provide an extended investigation of the maximum throughput achievable in input-queueing (IQ) or combined-input-and-output-queueing (CIOQ) packet switches. Some scheduling policies, among which are maximum weight matching algorithms, were identified as optimal, in the sense that they were proved to achieve 100% throughput under any admissible single-class traffic pattern. Most of the results in the literature, however, consider just one switch in isolation, operating on packets belonging to a single traffic class. In this paper we first generalize known results, showing that a wide class of IQ schedulers operating on multiple traffic classes can achieve 100% throughput. In addition, we address the problem of the maximum throughput achievable in a network of interconnected IQ switches loaded by multiclass traffic, and we devise some simple scheduling policies that guarantee 100% throughput when switches are interconnected in a network. Both the Lyapunov function methodology and the fluid models approach are used to obtain our results.