Heavy traffic analysis of approximate max-weight matching algorithms for input-queued switches

In this paper, we propose a class of approximation algorithms for the max-weight matching (MWM) policy for input-queued switches, called expected 1-APRX. We establish the state space collapse (SSC) result for expected 1-APRX, and characterize its queue length behavior in the heavy-traffic limit. Our results indicate that expected 1-APRX can approximately approach the optimal queue length scaling in the heavy-traffic regime. We further propose an expected 1-APRX based policy, called MWM with adaptive update (MWM-AU), for reducing communication cost due to queue information update. We prove that MWM-AU is throughput optimal and characterize its heavy-traffic limit behavior. Our simulation results demonstrate that the proposed policy can significantly reduce queue update overhead, while maintaining the delay performance comparable to that of MWM. (C) 2020 Elsevier B.V. All rights reserved.