Is Tail-Optimal Scheduling Possible?

This paper focuses on the competitive analysis of scheduling disciplines in a large deviations setting. Although there are policies that are known to optimize the sojourn time tail under a large class of heavy-tailed job sizes (e.g., processor sharing and shortest remaining processing time) and there are policies known to optimize the sojourn time tail in the case of light-tailed job sizes (e.g., first come first served), no policies are known that can optimize the sojourn time tail across both light- and heavy-tailed job size distributions. We prove that no such work-conserving, nonanticipatory, nonlearning policy exists, and thus that a policy must learn (or know) the job size distribution in order to optimize the sojourn time tail

Scheduling for the tail: Robustness versus optimality

When scheduling to minimize the sojourn time tail, the goals of optimality and robustness are seemingly at odds. Over the last decade, results have emerged which show that scheduling disciplines that are near-optimal under light (exponential) tailed workload distributions do not perform well under heavy (power) tailed workload distributions, and vice-versa. Very recently, it has been shown that this conflict between optimality and robustness is fundamental, i.e., no policy that does not learn information about the workload can be optimal across both light-tailed and heavy-tailed workloads. In this paper we show that one can exploit very limited workload information (the system load) in order to design a scheduler that provides robust performance across heavy-tailed and light-tailed workloads

Characterizing Policies with Optimal Response Time Tails under Heavy-Tailed Job Sizes

We consider the tail behavior of the response time distribution in an M/G/1 queue with heavy-tailed job sizes, specifically those with intermediately regularly varying tails. In this setting, the response time tail of many individual policies has been characterized, and it is known that policies such as Shortest Remaining Processing Time (SRPT) and Foreground-Background (FB) have response time tails of the same order as the job size tail, and thus such policies are tail-optimal. Our goal in this work is to move beyond individual policies and characterize the set of policies that are tail-optimal. Toward that end, we use the recently introduced SOAP framework to derive sufficient conditions on the form of prioritization used by a scheduling policy that ensure the policy is tail-optimal. These conditions are general and lead to new results for important policies that have previously resisted analysis, including the Gittins policy, which minimizes mean response time among policies that do not have access to job size information. As a by-product of our analysis, we derive a general upper bound for fractional moments of M/G/1 busy periods, which is of independent interest

Achievable performance of blind policies in heavy traffic

For a GI/GI/1 queue, we show that the average sojourn time under the (blind) Randomized Multilevel Feedback algorithm is no worse than that under the Shortest Remaining Processing Time algorithm times a logarithmic function of the system load. Moreover, it is verified that this bound is tight in heavy traffic, up to a constant multiplicative factor. We obtain this result by combining techniques from two disparate areas: competitive analysis and applied probability