research-article

Delay Asymptotics and Bounds for Multi-Task Parallel Jobs

Authors:

Mor Harchol-Balter,

Alan Scheller-Wolf,

R. SrikantAuthors Info & Claims

ACM SIGMETRICS Performance Evaluation Review, Volume 46, Issue 3

Pages 2 - 7

https://doi.org/10.1145/3308897.3308901

Published: 25 January 2019 Publication History

Abstract

We study delay of jobs that consist of multiple parallel tasks, which is a critical performance metric in a wide range of applications such as data file retrieval in coded storage systems and parallel computing. In this problem, each job is completed only when all of its tasks are completed, so the delay of a job is the maximum of the delays of its tasks. Despite the wide attention this problem has received, tight analysis is still largely unknown since analyzing job delay requires characterizing the complicated correlation among task delays, which is hard to do.

We first consider an asymptotic regime where the number of servers, n, goes to infinity, and the number of tasks in a job, k(n), is allowed to increase with n. We establish the asymptotic independence of any k(n) queues under the condition k(n) = o(n1/4). This greatly generalizes the asymptotic-independence type of results in the literature where asymptotic independence is shown only for a fixed constant number of queues. As a consequence of our independence result, the job delay converges to the maximum of independent task delays.

We next consider the non-asymptotic regime. Here we prove that independence yields a stochastic upper bound on job delay for any n and any k(n) with k(n)≤n. The key component of our proof is a new technique we develop, called "Poisson oversampling". Our approach converts the job delay problem into a corresponding balls-and-bins problem. However, in contrast with typical balls-and-bins problems where there is a negative correlation among bins, we prove that our variant exhibits positive correlation. A full version of this paper will all proofs appears in [28].

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Cited By

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https://doi.org/10.3390/math12050659
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Published In

cover image ACM SIGMETRICS Performance Evaluation Review

ACM SIGMETRICS Performance Evaluation Review Volume 46, Issue 3

December 2018

174 pages

ISSN:0163-5999

DOI:10.1145/3308897

Editor:
Nidhi Hegde
Borealis AI

Issue’s Table of Contents

Copyright © 2019 Copyright is held by the owner/author(s).

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Published: 25 January 2019

Published in SIGMETRICS Volume 46, Issue 3

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Cited By

Vishnevsky VKlimenok VSokolov ALarionov A(2024)Investigation of the Fork–Join System with Markovian Arrival Process Arrivals and Phase-Type Service Time Distribution Using Machine Learning MethodsMathematics10.3390/math1205065912:5(659)Online publication date: 23-Feb-2024
https://doi.org/10.3390/math12050659
Barron Y(2023)The Delay Time Profile of Multistage Networks with SynchronizationMathematics10.3390/math1114323211:14(3232)Online publication date: 23-Jul-2023
https://doi.org/10.3390/math11143232
Alshahrani RPeyravi H(2021)Modeling and analysis of distributed schedulers in data center cluster networksCluster Computing10.1007/s10586-021-03343-y24:4(3351-3366)Online publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1007/s10586-021-03343-y
Zubeldia M(2020)Delay-optimal Policies in Partial Fork-Join Systems with Redundancy and Random SlowdownsProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/33794684:1(1-49)Online publication date: 5-Jun-2020
https://dl.acm.org/doi/10.1145/3379468
Althoubi AAlshahrani RPeyravi H(2020)Tail Latency in Datacenter NetworksModelling, Analysis, and Simulation of Computer and Telecommunication Systems10.1007/978-3-030-68110-4_17(254-272)Online publication date: 17-Nov-2020
https://dl.acm.org/doi/10.1007/978-3-030-68110-4_17
Hellemans TBodas TVan Houdt B(2019)Performance Analysis of Workload Dependent Load Balancing PoliciesProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/3341617.33261503:2(1-35)Online publication date: 19-Jun-2019
https://dl.acm.org/doi/10.1145/3341617.3326150
Hellemans TBodas TVan Houdt BNahum EBonald TDuffield N(2019)Performance Analysis of Workload Dependent Load Balancing PoliciesAbstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems10.1145/3309697.3331504(7-8)Online publication date: 20-Jun-2019
https://dl.acm.org/doi/10.1145/3309697.3331504
Al-Abbasi AAggarwal VLan T(2019)TTLoC: Taming Tail Latency for Erasure-Coded Cloud Storage SystemsIEEE Transactions on Network and Service Management10.1109/TNSM.2019.291687716:4(1609-1623)Online publication date: Dec-2019
https://doi.org/10.1109/TNSM.2019.2916877

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