Open AccessOpen Access licenseAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail Go to SectionOpen AccessOpen Access license HomeStochastic SystemsVol. 1, No. 1 Diffusion Limits for Shortest Remaining Processing Time QueuesH. Christian Gromoll, Łukasz Kruk, Amber L. PuhaH. Christian Gromoll, Łukasz Kruk, Amber L. PuhaPublished Online:6 Feb 2011https://doi.org/10.1287/10-SSY016AbstractWe present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy traffic assumptions, we prove a diffusion limit theorem for a measure-valued state descriptor, from which we conclude a similar theorem for the queue length process. These results allow us to make some observations on the queue length optimality of SRPT. In particular, they provide the sharpest illustration of the well-known tension between queue length optimality and quality of service for this policy. Back to Top Next FiguresReferencesRelatedInformationCited BySRPT Scheduling Discipline in Many-Server Queues with Impatient CustomersJing Dong, Rouba Ibrahim21 October 2021 | Management Science, Vol. 67, No. 12Fluid Limits for Multiple-Input Shortest Remaining Processing Time QueuesŁukasz Kruk, Ewa Sokołowska21 April 2016 | Mathematics of Operations Research, Vol. 41, No. 3 Volume 1, Issue 1June 2011Pages 1-208 Article Information Metrics Downloaded 68 times in the past 12 months Information Received:October 01, 2010Published Online:February 06, 2011 Copyright © 2011, The author(s)Cite asH. Christian Gromoll, Łukasz Kruk, Amber L. Puha (2011) Diffusion Limits for Shortest Remaining Processing Time Queues. Stochastic Systems 1(1):1-16. https://doi.org/10.1287/10-SSY016 KeywordsHeavy trafficqueueingshortest remaining processing timediffusion limitPDF download