Simple Near-Optimal Scheduling for the M/G/1

Scully, Ziv; Scheller‐Wolf, Alan

doi:10.1145/3379477

“…The tail optimality of M-SERPT is particularly significant because M-SERPT has mean response time within a factor of 5 of Gittins's [29], and is simpler to understand and implement. Moreover, unlike our result for Gittins in Corollary 3.5, we require no additional assumptions on the job size distribution to ensure M-SERPT's tail optimality.…”

Section: Shortest Expected Remaining Processing Timementioning

confidence: 99%

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

Scully

¹

,

Kreveld

²

,

Boxma

³

et al. 2020

Proc. ACM Meas. Anal. Comput. Syst.

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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.

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“…2.2. This suggests that SERPT may be a good Gittins substitute, and there is theoretical evidence supporting this [29]. This is certainly true for the job size distribution from Fig.…”

Section: E[t]/e[tgiins]mentioning

confidence: 59%

“…Unfortunately, Gittins is a complicated policy. Implementing Gittins requires solving an optimization problem at every age 𝑎, and these optimization problems are hard to solve in general [29,Appendix B].…”

Section: Creating a Gittins Substitutementioning

confidence: 99%

How to Schedule Near-Optimally under Real-World Constraints

Scully¹

2021

Preprint

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Scheduling is a critical part of practical computer systems, and scheduling has also been extensively studied from a theoretical perspective. Unfortunately, there is a gap between theory and practice, as the optimal scheduling policies presented by theory can be difficult or impossible to perfectly implement in practice. In this work, we use recent breakthroughs in queueing theory to begin to bridge this gap. We show how to translate theoretically optimal policies-which provably minimize mean response time (a.k.a. latency)-into near-optimal policies that are easily implemented in practical settings. Specifically, we handle the following real-world constraints:• We show how to schedule in systems where job sizes (a.k.a. running times) are unknown, or only partially known. We do so using simple policies that achieve performance very close to the much more complicated theoretically optimal policies. • We show how to schedule in systems that have only a limited number of priority levels available. We show how to adapt theoretically optimal policies to this constrained setting and determine how many levels we need for near-optimal performance. • We show how to schedule in systems where job preemption can only happen at specific checkpoints.Adding checkpoints allows for smarter scheduling, but each checkpoint incurs time overhead. We give a rule of thumb that near-optimally balances this tradeoff.

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“…The Monotonic SERPT (M-SERPT) policy is a variant of SERPT introduced by Scully et al [29]. Its rank function is the increasing envelope of SERPT's:…”

Section: Shortest Expected Remaining Processing Timementioning

confidence: 99%

“…As with SERPT, Lemma 2.2 implies r (a) ∈ Ω(a) ∩O(a) for M-SERPT, so M-SERPT is also tail-optimal. The tail optimality of M-SERPT is particularly significant because M-SERPT has mean response time within a factor of 5 of Gittins's [29], and is simpler to understand and implement. Moreover, unlike our result for Gittins in Corollary 3.5, we require no additional assumptions on the job size distribution to ensure M-SERPT's tail optimality.…”

Section: Shortest Expected Remaining Processing Timementioning

confidence: 99%

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

Scully

¹

,

Kreveld

²

,

Boxma

³

et al. 2020

SIGMETRICS Perform. Eval. Rev.

Self Cite

0

View full text Add to dashboard Cite

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. CCS Concepts: • General and reference → Performance; • Mathematics of computing → Queueing theory; • Networks → Network performance modeling; • Computing methodologies → Model development and analysis; • Software and its engineering → Scheduling.

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Simple Near-Optimal Scheduling for the M/G/1

Cited by 15 publications

References 28 publications

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

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

How to Schedule Near-Optimally under Real-World Constraints

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

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