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

Abstract

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.