Nudge: Stochastically Improving upon FCFS

The First-Come First-Served (FCFS) scheduling policy is the most popular algorithm used in practice. Furthermore, its usage 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 tail? What also 99th percentile time, or fraction jobs that complete under one second? Is still best? Outside regime, only loose bounds on are known, and optimality completely open. In this paper, introduce a new policy, Nudge, which first to provably stochastically improve upon FCFS. We prove Nudge simultaneously improves at every point along tail, distributions. As result, outperforms moment Moreover, provides multiplicative improvement over tail. This resolves long-standing open problem by showing that, counter previous conjecture, not strongly asymptotically optimal.