Degree of Queue Imbalance

Abstract

In this paper, we argue that heavy-traffic delay optimality is a coarse metric that does not necessarily imply good delay performance. Specifically, we show that any load balancing scheme is heavy-traffic delay optimal as long as it satisfies a fairly weak condition. This condition only requires that in the long-term the dispatcher favors, even slightly, shorter queues over longer queues. Hence, the empirical delay performance of heavy-traffic delay optimal schemes can range from very good (that of join-shortest-queue) to very bad (arbitrarily close to the performance of random routing).