Invariance of fluid limits for the Shortest Remaining Processing Time and Shortest Job First policies

TL;DR

This paper proves that the fluid limits of SRPT and SJF queueing policies are identical, showing that SJF, a simpler policy, asymptotically matches SRPT's queue length and response time performance.

Contribution

It establishes the invariance of fluid limits between SRPT and SJF policies, demonstrating the asymptotic equivalence in performance for queue length and response times.

Findings

Fluid limits of SRPT and SJF are identical.

SJF achieves queue length optimality asymptotically.

Both policies have the same response time performance on fluid scale.

Abstract

We consider a single-server queue with renewal arrivals and i.i.d. service times, in which the server employs either the preemptive Shortest Remaining Processing Time (SRPT) policy, or its non-preemptive variant, Shortest Job First (SJF). We show that for given stochastic primitives (initial condition, arrival and service processes), the model has the same fluid limit under either policy. In particular, we conclude that the well-known queue length optimality of preemptive SRPT is also achieved, asymptotically on fluid scale, by the simpler-to-implement SJF policy. We also conclude that on fluid scale, SJF and SRPT achieve the same performance with respect to response times of the longest-waiting jobs in the system.