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State-dependent response times via fluid limits in shortest remaining processing time queues

Authors:

Douglas G. Down,

H. Christian Gromoll,

Amber L. PuhaAuthors Info & Claims

ACM SIGMETRICS Performance Evaluation Review, Volume 37, Issue 2

Pages 75 - 76

https://doi.org/10.1145/1639562.1639593

Published: 16 October 2009 Publication History

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Abstract

We consider a single server queue with renewal arrivals and i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. We provide a fluid model (or formal law of large numbers approximation) for this system. The foremost payoff of our fluid model is a fluid level approximation for the state-dependent response time of a job of arbitrary size, that is, the amount of time it spends in the system, given an arbitrary system configuration at the time of its arrival.

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D.G. Down, H.C. Gromoll and A.L. Puha. Fluid limits for shortest remaining processing time queues. Mathematics of Operations Research forthcoming.

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M. Nuyens, A. Wierman and B. Zwart. Preventing large sojourn times using SMART scheduling. Operations Research 56: 88--101, 2008.

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L. Schrage. A proof of the optimality of the shortest remaining processing time discipline. Operations Research 16: 687--690, 1968.

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Banerjee SBudhiraja APuha A(2022)Heavy traffic scaling limits for shortest remaining processing time queues with heavy tailed processing time distributionsThe Annals of Applied Probability10.1214/21-AAP174132:4Online publication date: 1-Aug-2022
https://doi.org/10.1214/21-AAP1741
Pender JSudhakar SZhang E(2021)Combining simulation and machine learning for response time prediction for the shortest remaining processing time disciplineProceedings of the Winter Simulation Conference10.5555/3522802.3522847(1-12)Online publication date: 13-Dec-2021
https://dl.acm.org/doi/10.5555/3522802.3522847
Pender JSudhakar SZhang E(2021)Combining Simulation and Machine Learning for Response Time Prediction for the Shortest Remaining Processing Time Discipline2021 Winter Simulation Conference (WSC)10.1109/WSC52266.2021.9715439(1-12)Online publication date: 12-Dec-2021
https://doi.org/10.1109/WSC52266.2021.9715439
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State-dependent response times via fluid limits in shortest remaining processing time queues

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Published In

cover image ACM SIGMETRICS Performance Evaluation Review

ACM SIGMETRICS Performance Evaluation Review Volume 37, Issue 2

September 2009

89 pages

ISSN:0163-5999

DOI:10.1145/1639562

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Association for Computing Machinery

New York, NY, United States

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Published: 16 October 2009

Published in SIGMETRICS Volume 37, Issue 2

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Banerjee SBudhiraja APuha A(2022)Heavy traffic scaling limits for shortest remaining processing time queues with heavy tailed processing time distributionsThe Annals of Applied Probability10.1214/21-AAP174132:4Online publication date: 1-Aug-2022
https://doi.org/10.1214/21-AAP1741
Pender JSudhakar SZhang E(2021)Combining simulation and machine learning for response time prediction for the shortest remaining processing time disciplineProceedings of the Winter Simulation Conference10.5555/3522802.3522847(1-12)Online publication date: 13-Dec-2021
https://dl.acm.org/doi/10.5555/3522802.3522847
Pender JSudhakar SZhang E(2021)Combining Simulation and Machine Learning for Response Time Prediction for the Shortest Remaining Processing Time Discipline2021 Winter Simulation Conference (WSC)10.1109/WSC52266.2021.9715439(1-12)Online publication date: 12-Dec-2021
https://doi.org/10.1109/WSC52266.2021.9715439
Kruk ŁSokołowska E(2016)Fluid Limits for Multiple-Input Shortest Remaining Processing Time QueuesMathematics of Operations Research10.1287/moor.2015.076841:3(1055-1092)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1287/moor.2015.0768
Gromoll HKeutel M(2012)Invariance of fluid limits for the shortest remaining processing time and shortest job first policiesQueueing Systems: Theory and Applications10.1007/s11134-011-9267-570:2(145-164)Online publication date: 1-Feb-2012
https://dl.acm.org/doi/10.1007/s11134-011-9267-5
Gromoll HKruk ŁPuha A(2011)Diffusion Limits for Shortest Remaining Processing Time QueuesStochastic Systems10.1287/10-SSY0161:1(1-16)Online publication date: Jun-2011
https://doi.org/10.1287/10-SSY016

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Fluid Limits for Multiple-Input Shortest Remaining Processing Time Queues

Analyzing state-dependent arrival in GI/BMSP/1/∞ queues

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