SRPT for Multiserver Systems

TL;DR

This paper provides the first stochastic analysis of multiserver SRPT, demonstrating its asymptotic optimality in mean response time in heavy traffic, and extends results to other multiserver policies.

Contribution

It introduces the first stochastic bounds for multiserver SRPT and proves its asymptotic optimality, filling a key gap in multiserver scheduling theory.

Findings

Multiserver SRPT has asymptotically optimal mean response time in heavy traffic.

The paper develops new stochastic bounds combining stochastic and worst-case techniques.

Similar bounds and optimality results are established for other multiserver scheduling policies.

Abstract

The Shortest Remaining Processing Time (SRPT) scheduling policy and its variants have been extensively studied in both theoretical and practical settings. While beautiful results are known for single-server SRPT, much less is known for multiserver SRPT. In particular, stochastic analysis of the M/G/k under multiserver SRPT is entirely open. Intuition suggests that multiserver SRPT should be optimal or near-optimal for minimizing mean response time. However, the only known analysis of multiserver SRPT is in the worst-case adversarial setting, where SRPT can be far from optimal. In this paper, we give the first stochastic analysis bounding mean response time of the M/G/k under multiserver SRPT. Using our response time bound, we show that multiserver SRPT has asymptotically optimal mean response time in the heavy-traffic limit. The key to our bounds is a strategic combination of stochastic and worst-case techniques. Beyond SRPT, we prove similar response time bounds and optimality results for several other multiserver scheduling policies.