Designing Low-Complexity Heavy-Traffic Delay-Optimal Load Balancing Schemes

In this paper, we establish a unified analytical framework for designing load balancing algorithms that can simultaneously achieve low latency, low complexity, and low communication overhead. We first propose a general class \Pi of load balancing policies and prove that they are throughput optimal and heavy-traffic delay optimal. This class \Pi includes popular policies such as join-shortest-queue (JSQ) and power-of- d as special cases, but not the recently proposed join-idle-queue (JIQ) policy. In fact, we show that JIQ is not heavy-traffic delay optimal even for homogeneous servers. By exploiting the flexibility offered by the class \Pi , we design a new load balancing policy called join-below-threshold (JBT-d), in which the arrival jobs are preferably assigned to queues that are no greater than a threshold, and the threshold is updated infrequently. JBT-d has several benefits: (i) JBT-d belongs to the class \Pi and hence is throughput optimal and heavy-traffic delay optimal. (ii) JBT-d has zero dispatching delay, like JIQ and other pull-based policies, and low message overhead due to infrequent threshold update. (iii) Extensive simulations show that JBT-d has excellent delay performance, comparable to the JSQ policy in various system settings.