Fluid limit for a multi-server, multiclass random order of service queue with reneging and tracking of residual patience times

Eva H. Loeser () and Ruth J. Williams ()
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Eva H. Loeser: University of California, San Diego
Ruth J. Williams: University of California, San Diego

Queueing Systems: Theory and Applications, 2025, vol. 109, issue 2, No 2, 78 pages

Abstract: Abstract In this paper, we consider a multi-server, multiclass queue with reneging operating under the random order of service discipline. Interarrival times, service times, and patience times are assumed to be generally distributed. Under mild conditions, we establish a fluid limit theorem for a measure-valued process that keeps track of the remaining patience time for each job in the queue, when the number of servers and classes is held fixed. We prove uniqueness for fluid model solutions in all but one case. We characterize the unique invariant state for the fluid model and prove that fluid model solutions converge to the invariant state as time goes to infinity, uniformly for suitable initial conditions.

Keywords: Random-order-of-service; Reneging; Queueing; Measure-valued; Fluid model; Primary 60K25; Secondary 68M20; 90B22 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11134-025-09941-6

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