Strongly Tail-Optimal Scheduling in the Light-Tailed M/G/1

Abstract

We study the problem of scheduling jobs in a queueing system, specifically an M/G/1 with light-tailed job sizes, to asymptotically optimize the response time tail. This means scheduling to make \mathbfP [T > t], the chance a job's response time exceeds t, decay as quickly as possible in the t → ∞ limit. For some time, the best known policy was First-Come First-Served (FCFS), which has an asymptotically exponential tail: P [T > t] ∼ C e -γ t . FCFS achieves the optimal decay rate ~γ, but its tail constant C is suboptimal. We derive a closed-form expression for the optimal tail constant, and we introduce γ-Boost, a new policy that achieves this optimal tail constant. We also show via simulation that γ-Boost has excellent practical performance. This abstract summarizes our full paper.