Outperforming Multiserver SRPT at All Loads

TL;DR

This paper introduces SEK-SMOD, a new multiserver scheduling policy that provably outperforms SRPT-$k$ in mean response time across all loads and distributions, using hybrid analysis techniques.

Contribution

We propose SEK-SMOD, the first policy to outperform SRPT-$k$ in all regimes, and develop a novel hybrid analysis method to prove its superiority.

Findings

SEK-SMOD outperforms SRPT-$k$ in mean response time across all loads.

Practical-SEK, a simplified version, also shows improved performance in simulations.

The new policy leverages large job prioritization to enhance server utilization.

Abstract

A well-designed scheduling policy can unlock significant performance improvements with no additional resources. Multiserver SRPT (SRPT-$k$) is known to achieve asymptotically optimal mean response time in the heavy traffic limit, as load approaches capacity. No better policy is known for the M/G/$k$ queue in any regime. We introduce a new policy, SRPT-Except-$k+1$ & Modified SRPT (SEK-SMOD), which is the first policy to provably achieve lower mean response time than SRPT-$k$. SEK-SMOD outperforms SRPT-$k$ across all loads and all job size distributions. The key idea behind SEK-SMOD is to prioritize large jobs over small jobs in specific scenarios to improve server utilization, and thereby improve the response time of subsequent jobs in expectation. Our proof is a novel application of hybrid worst-case and stochastic techniques to relative analysis, where we analyze the deviations of our proposed SEK-SMOD policy away from the SRPT-$k$ baseline policy. Furthermore, we design Practical-SEK (a simplified variant of SEK-SMOD) and empirically verify the improvement over SRPT-$k$ via simulation.