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We present an analysis of large-scale load balancing systems, where theprocessing time distribution of tasks depends on both the task and servertypes. Our study focuses on the asymptotic regime, where the number of serversand task types tend to infinity in proportion. In heterogeneous environments,commonly used load balancing policies such as Join Fastest Idle Queue and JoinFastest Shortest Queue exhibit poor performance and even shrink the stabilityregion. Interestingly, prior to this work, finding a scalable policy with aprovable performance guarantee in this setup remained an open question.  To address this gap, we propose and analyze two asymptotically delay-optimaldynamic load balancing policies. The first policy efficiently reserves theprocessing capacity of each server for ``good" tasks and routes tasks using thevanilla Join Idle Queue policy. The second policy, called the speed-prioritypolicy, significantly increases the likelihood of assigning tasks to therespective ``good" servers capable of processing them at high speeds. Byleveraging a framework inspired by the graphon literature and employing themean-field method and stochastic coupling arguments, we demonstrate that bothpolicies achieve asymptotic zero queuing. Specifically, as the system scales,the probability of a typical task being assigned to an idle server approaches1.

Optimal Rate-Matrix Pruning For Large-Scale Heterogeneous Systems