Fluid limits for overloaded multiclass FIFO single-server queues with general abandonment

Abstract

Open AccessOpen Access licenseAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail Go to SectionOpen AccessOpen Access license HomeStochastic SystemsVol. 3, No. 1 Fluid Limits for Overloaded Multiclass FIFO Single-Server Queues with General AbandonmentOtis B. Jennings, Amber L. PuhaOtis B. Jennings, Amber L. PuhaPublished Online:9 Aug 2013https://doi.org/10.1287/12-SSY085AbstractWe consider an overloaded multiclass nonidling first-in-first-out single-server queue with abandonment. The interarrival times, service times, and deadline times are sequences of independent and identically, but generally distributed random variables. In prior work, Jennings and Reed studied the workload process associated with this queue. Under mild conditions, they establish both a functional law of large numbers and a functional central limit theorem for this process. We build on that work here. For this, we consider a more detailed description of the system state given by K finite, nonnegative Borel measures on the nonnegative quadrant, one for each job class. For each time and job class, the associated measure has a unit atom associated with each job of that class in the system at the coordinates determined by what are referred to as the residual virtual sojourn time and residual patience time of that job. Under mild conditions, we prove a functional law of large numbers for this measure-valued state descriptor. This yields approximations for related processes such as the queue lengths and abandoning queue lengths. An interesting characteristic of these approximations is that they depend on the deadline distributions in their entirety. Previous Back to Top FiguresReferencesRelatedInformationCited byA Dynamic Network Model of Interbank Lending—Systemic Risk and Liquidity ProvisioningAgostino Capponi, Xu Sun, David D. Yao7 April 2020 | Mathematics of Operations Research, Vol. 45, No. 3 Volume 3, Issue 1June 2013Pages 1-321 Article Information Metrics Information Received:October 01, 2012Published Online:August 09, 2013 Copyright © 2013, The author(s)Cite asOtis B. Jennings, Amber L. Puha (2013) Fluid Limits for Overloaded Multiclass FIFO Single-Server Queues with General Abandonment. Stochastic Systems 3(1):262-321. https://doi.org/10.1287/12-SSY085 KeywordsOverloaded queueabandonmentfirst-in-first-outmulticlass queuemeasure-valued state descriptorqueue-length vectorfluid limitsfluid modelinvariant statesPDF download