Nudge: Stochastically Improving upon FCFS

Abstract

The First-Come First-Served (FCFS) scheduling policy is the most popular scheduling algorithm used in practice. Furthermore, its usage is theoretically validated: for light-tailed job size distributions, FCFS has weakly optimal asymptotic tail of response time. But what if we don't just care about the asymptotic tail≥ What if we also care about the 99th percentile of response time, or the fraction of jobs that complete in under one second≥ Is FCFS still best≥ Outside of the asymptotic regime, only loose bounds on the tail of FCFS are known, and optimality is completely open. In this paper, we introduce a new policy, Nudge, which is the first policy to provably stochastically improve upon FCFS. We prove that Nudge simultaneously improves upon FCFS at every point along the tail, for light-tailed job size distributions. As a result, Nudge outperforms FCFS for every moment and every percentile of response time. Moreover, Nudge provides a multiplicative improvement over FCFS in the asymptotic tail. This resolves a long-standing open problem by showing that, counter to previous conjecture, FCFS is not strongly asymptotically optimal.