Optimal Scheduling in the Multiserver-job Model under Heavy Traffic

TL;DR

This paper introduces the ServerFilling-SRPT policy that minimizes mean response time in multiserver-job systems under heavy traffic, outperforming existing policies, and also proposes ServerFilling-Gittins for unknown job sizes.

Contribution

It presents the first scheduling policy proven to minimize mean response time in multiserver-job systems under heavy traffic conditions.

Findings

ServerFilling-SRPT outperforms existing policies at high loads.

The policy is proven optimal in the heavy traffic limit.

Empirical results show orders of magnitude improvement at high loads.

Abstract

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. In simpler settings, such as various known-size single-server-job settings, minimizing mean response time is merely a matter of prioritizing small jobs. However, for the multiserver-job system, prioritizing small jobs is not enough, because we must also ensure servers are not unnecessarily left idle. Thus, minimizing mean response time requires prioritizing small jobs while simultaneously maximizing throughput. 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 improvements by orders of magnitude at higher loads. Because ServerFilling-SRPT requires knowing job sizes, we also define the ServerFilling-Gittins policy, which is optimal when sizes are unknown or partially known.