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 maximizing utilization, with almost nothing known about mean response time. In simpler settings, such as various known-size single-server-job minimizing time is merely a matter prioritizing small jobs. However, for system, not enough, because we must also ensure servers are unnecessarily left idle. Thus, requires while simultaneously throughput. Our question how to achieve these joint objectives. We devise ServerFilling-SRPT scheduling policy, which first policy minimize model heavy traffic limit. addition proving this heavy-traffic result, present empirical evidence that outperforms existing policies loads, improvements by orders magnitude higher loads. Because knowing job sizes, define ServerFilling-Gittins optimal when sizes unknown or partially known.