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We establish a unified analytical framework for load balancing systems, whichallows us to construct a general class $\Pi$ of policies that are boththroughput optimal and heavy-traffic delay optimal. This general class $\Pi$includes as special cases popular policies such as join-shortest-queue andpower-of-$d$, but not the join-idle-queue (JIQ) policy. In fact, we show thatJIQ, which is not in $\Pi$, is actually not heavy-traffic delay optimal. Owingto the significant flexibility offered by class $\Pi$, we are able to design anew policy called join-below-threshold (JBT-d), which maintains the simplicityof pull-based policies such as JIQ, but updates its threshold dynamically. Weprove that JBT-$d$ belongs to the class $\Pi$ when the threshold is pickedappropriately and thus it is heavy-traffic delay optimal. Extensive simulationsshow that the new policy not only has a low complexity in message rates, butalso achieves excellent delay performance, comparable to the optimaljoin-shortest-queue in various system settings.

Designing Low-Complexity Heavy-Traffic Delay-Optimal Load Balancing Schemes: Theory to Algorithms