Benjamin Berg, Jan-Pieter L. Dorsman, Mor Harchol-Balter
To keep pace with Moore's law, chip designers have focused on increasing the number of cores per chip. To effectively leverage these multi-core chips, one must decide how many cores to assign to each job. Given that jobs receive sublinear speedups from additional cores, there is a tradeoff: allocating more cores to an individual job reduces the job's runtime, but decreases the efficiency of the overall system. We ask how the system should assign cores to jobs so as to minimize the mean response time over a stream of incoming jobs. To answer this question, we develop an analytical model of jobs running on a multi-core machine. We prove that EQUI, a policy which continuously divides cores evenly across jobs, is optimal when all jobs follow a single speedup curve and have exponentially distributed sizes. We also consider a class of "fixed-width" policies, which choose a single level of parallelization, k, to use for all jobs. We prove that, surprisingly, fixed-width policies which use the optimal fixed level of parallelization, k*, become near-optimal as the number of cores becomes large. In the case where jobs may follow different speedup curves, finding a good scheduling policy is even more challenging. In particular, EQUI is no longer optimal, but a very simple policy, GREEDY*, performs well empirically.
{"title":"Towards Optimality in Parallel Job Scheduling","authors":"Benjamin Berg, Jan-Pieter L. Dorsman, Mor Harchol-Balter","doi":"10.1145/3219617.3219666","DOIUrl":"https://doi.org/10.1145/3219617.3219666","url":null,"abstract":"To keep pace with Moore's law, chip designers have focused on increasing the number of cores per chip. To effectively leverage these multi-core chips, one must decide how many cores to assign to each job. Given that jobs receive sublinear speedups from additional cores, there is a tradeoff: allocating more cores to an individual job reduces the job's runtime, but decreases the efficiency of the overall system. We ask how the system should assign cores to jobs so as to minimize the mean response time over a stream of incoming jobs. To answer this question, we develop an analytical model of jobs running on a multi-core machine. We prove that EQUI, a policy which continuously divides cores evenly across jobs, is optimal when all jobs follow a single speedup curve and have exponentially distributed sizes. We also consider a class of \"fixed-width\" policies, which choose a single level of parallelization, k, to use for all jobs. We prove that, surprisingly, fixed-width policies which use the optimal fixed level of parallelization, k*, become near-optimal as the number of cores becomes large. In the case where jobs may follow different speedup curves, finding a good scheduling policy is even more challenging. In particular, EQUI is no longer optimal, but a very simple policy, GREEDY*, performs well empirically.","PeriodicalId":210440,"journal":{"name":"Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134547570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Distributed network optimization has been studied several years. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality, convergence speed, and delay. To address these challenges, in this paper, we propose a new algorithmic framework with all these metrics approaching optimality. The salient features of our new algorithm are three-fold: (i) fast convergence: it converges with only O(log(1/ε)) iterations, that is the fastest speed among all the existing algorithms; (ii) low delay: it guarantees optimal utility with finite queue length; (iii) simple implementation: the control variables of this algorithm are based on virtual queues that do not require maintaining per-flow information. The new technique builds on a kind of inexact Uzawa method in the Alternating Directional Method of Multiplier. A theoretical contribution of independent interest is a new pathway we provide to prove global and linear convergence rate of Uzawa-ADMM without requiring the full rank assumption of the constraint matrix.
{"title":"Towards Fast-Convergence, Low-Delay and Low-Complexity Network Optimization","authors":"Sinong Wang, N. Shroff","doi":"10.1145/3219617.3219671","DOIUrl":"https://doi.org/10.1145/3219617.3219671","url":null,"abstract":"Distributed network optimization has been studied several years. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality, convergence speed, and delay. To address these challenges, in this paper, we propose a new algorithmic framework with all these metrics approaching optimality. The salient features of our new algorithm are three-fold: (i) fast convergence: it converges with only O(log(1/ε)) iterations, that is the fastest speed among all the existing algorithms; (ii) low delay: it guarantees optimal utility with finite queue length; (iii) simple implementation: the control variables of this algorithm are based on virtual queues that do not require maintaining per-flow information. The new technique builds on a kind of inexact Uzawa method in the Alternating Directional Method of Multiplier. A theoretical contribution of independent interest is a new pathway we provide to prove global and linear convergence rate of Uzawa-ADMM without requiring the full rank assumption of the constraint matrix.","PeriodicalId":210440,"journal":{"name":"Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116487421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Learning II","authors":"D. Shah","doi":"10.1145/3258592","DOIUrl":"https://doi.org/10.1145/3258592","url":null,"abstract":"","PeriodicalId":210440,"journal":{"name":"Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125500759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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