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

Scully, Ziv; Kreveld, Lucas van; Boxma, Onno; Dorsman, Jan-Pieter; Wierman, Adam

doi:10.1145/3392148

Cited by 10 publications

(17 citation statements)

References 31 publications

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“…Moreover, many popular preemptive policies such as PS, SRPT, and Foreground-Background (FB) 3 are "weakly pessimal": they have the maximum possible asymptotic tail, up to a constant factor, of any work-conserving scheduling policy [25,26]. • For heavy-tailed job sizes, the reverse is true: PS, SRPT, FB, and similar policies are all weakly optimal [5,26,33], while FCFS is weakly pessimal.…”

Section: Asymptotic Tails: Extensive Theory But Open Problems Remainmentioning

confidence: 99%

Nudge: Stochastically Improving upon FCFS

GrosofIsaac¹,

YangKunhe²,

Scully³

et al. 2021

Proc. ACM Meas. Anal. Comput. Syst.

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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.

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Section: Asymptotic Tails: Extensive Theory But Open Problems Remainmentioning

confidence: 99%

Nudge: Stochastically Improving upon FCFS

GrosofIsaac¹,

YangKunhe²,

Scully³

et al. 2021

Proc. ACM Meas. Anal. Comput. Syst.

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“…We mention particularly the relation between this paper and [27]. Both papers consider response time tail behavior of arbitrary SOAP policies including the Gittins policy.…”

Section: Tail Optimality Of Certain Soap Policies In the Heavy-tailed...mentioning

confidence: 99%

“…The key tool we use to analyze Gittins's asymptotic response time tail is the SOAP framework [26,27]. SOAP gives a universal M/G/1 response time analysis of all SOAP policies, which are scheduling policies where a job's priority level is a function of its age (Definition 3.1).…”

Section: Contributionsmentioning

confidence: 99%

“…Much less is known about minimizing the tail of response time P[ > ], which is the probability a job has response time greater than a parameter ≥ 0. In light of the difficulty of studying the tail directly, theorists have studied the asymptotic tail of response time, which is the asymptotic decay of P[ > ] in the → ∞ limit [6,7,19,27,29]. In this work, we study the M/G/1, a classic single-server queueing model, and ask the following question.…”

Section: Introductionmentioning

confidence: 99%

“…• In the heavy-tailed case, Gittins has been shown to be tail-optimal, but only under an assumption on the job size distribution's hazard rate [27,Corollary 3.5]. • In the light-tailed case, Gittins sometimes reduces to FCFS or FB [2,3].…”

Section: Introductionmentioning

confidence: 99%

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When Does the Gittins Policy Have Asymptotically Optimal Response Time Tail?

Scully¹,

Kreveld²

2021

Preprint

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We consider scheduling in the M/G/1 queue with unknown job sizes. It is known that the Gittins policy minimizes mean response time in this setting. However, the behavior of the tail of response time under Gittins is poorly understood, even in the large-response-time limit. Characterizing Gittins's asymptotic tail behavior is important because if Gittins has optimal tail asymptotics, then it simultaneously provides optimal mean response time and good tail performance.In this work, we give the first comprehensive account of Gittins's asymptotic tail behavior. For heavy-tailed job sizes, we find that Gittins always has asymptotically optimal tail. The story for light-tailed job sizes is less clear-cut: Gittins's tail can be optimal, pessimal, or in between. To remedy this, we show that a modification of Gittins avoids pessimal tail behavior while achieving near-optimal mean response time.

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Frequency scaling in multilevel queues

Elahi

Marin

Rossi

et al. 2020

Performance Evaluation

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In this paper, we study a variant of PS+PS multilevel scheduling, which we call the PS+IS queue. Specifically, we use Processor Sharing (PS) at both queues, but with linear frequency scaling on the second queue, so that the latter behaves like an Infinite Server (IS) queue. The goals of the system are low response times for small jobs in the first queue, and reduced power consumption for large jobs in the second queue. The novelty of our model includes the frequency scaling at the second queue, and the batch arrival process at the second queue induced by the busy period structure of the first queue which has strictly higher priority. We derive a numerical solution for the PS+IS queueing system in steady-state, and then study its properties under workloads obtained from fitting of TCP flow traces. The simulation results confirm the e cacy of the PS+IS model. This article is an introduction to our longer paper in [5].

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

Cited by 10 publications

References 31 publications

Nudge: Stochastically Improving upon FCFS

Nudge: Stochastically Improving upon FCFS

When Does the Gittins Policy Have Asymptotically Optimal Response Time Tail?

Frequency scaling in multilevel queues

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