Tail-robust scheduling via limited processor sharing

From a rare events perspective, scheduling disciplines that work well under light (exponential) tailed workload distributions do not perform well under heavy (power) tailed workload distributions, and vice versa, leading to fundamental problems in designing schedulers that are robust to distributional assumptions on the job sizes. This paper shows how to exploit partial workload information (system load) to design a scheduler that provides robust performance across heavy-tailed and light-tailed workloads. Specifically, we derive new asymptotics for the tail of the stationary sojourn time under Limited Processor Sharing (LPS) scheduling for both heavy-tailed and light-tailed job size distributions, and show that LPS can be robust to the tail of the job size distribution if the multiprogramming level is chosen carefully as a function of the load.