Optimal Scheduling in the Multiserver-job Model under Heavy Traffic

Multiserver-job systems, where jobs require concurrent service at many servers, occur widely in practice. Essentially all of the theoretical work on multiserver-job systems focuses on maximizing utilization, with almost nothing known about mean response time. Our goal in this paper is to minimize mean response time in a multiserver-job setting. Minimizing mean response time requires prioritizing small jobs while simultaneously maximizing utilization. Our question is how to achieve these joint objectives. We devise the ServerFilling-SRPT scheduling policy, which is the first policy to minimize mean response time in the multiserver-job model in the heavy traffic limit. In addition to proving this heavy-traffic result, we present empirical evidence that ServerFilling-SRPT outperforms all existing scheduling policies for all loads, with orders of magnitude improvements at high load. Because ServerFilling-SRPT requires knowing job sizes, we also define the ServerFilling-Gittins policy, which is optimal when sizes are unknown or partially known. For more detail, see the full paper https://doi.org/10.1145/3570612