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

Scully, Ziv and van Kreveld, Lucas and Boxma, Onno and Dorsman, Jan-Pieter and Wierman, Adam (2020) Characterizing Policies with Optimal Response Time Tails under Heavy-Tailed Job Sizes. Proceedings of the ACM on Measurement and Analysis of Computing Systems, 4 (2). Art. No. 30. ISSN 2476-1249. doi:10.1145/3392148.

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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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Additional Information:© 2020 Association for Computing Machinery. ACM OPEN. Received January 2020; revised February 2020; accepted March 2020. The authors are grateful to Bert Zwart for providing some useful references. Ziv Scully was supported by an ARCS Foundation scholarship and the NSF Graduate Research Fellowship Program under Grant Nos. DGE-1745016 and DGE-125222. Lucas van Kreveld, Onno Boxma, and Jan-Pieter Dorsman were supported by the Netherlands Organisation for Scientific Research (NWO) through the Gravitation project NETWORKS, grant number 024.002.003. Adam Wierman was supported by NSF grant CNS-1518941.
Funding AgencyGrant Number
NSF Graduate Research FellowshipDGE-1745016
NSF Graduate Research FellowshipDGE-125222
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)024.002.003
Subject Keywords:response time; sojourn time; tail latency; tail optimality; Gittins policy; shortest expected processing time (SERPT); randomized multi-level feedback (RMLF); M/G/1
Issue or Number:2
Record Number:CaltechAUTHORS:20200511-093940097
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Official Citation:Ziv Scully, Lucas van Kreveld, Onno Boxma, Jan-Pieter Dorsman, and Adam Wierman. 2020. Characterizing Policies with Optimal Response Time Tails under Heavy-Tailed Job Sizes. Proc. ACM Meas. Anal. Comput. Syst. 4, 2, Article 30 (June 2020), 33 pages.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103094
Deposited By: Tony Diaz
Deposited On:11 May 2020 17:40
Last Modified:16 Nov 2021 18:18

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