Fluid Limits for Longest Remaining Time First Queues

Łukasz Kruk ()
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Łukasz Kruk: Institute of Mathematics, Maria Curie-Skłodowska University, 20-031 Lublin, Poland

Mathematics of Operations Research, 2024, vol. 49, issue 4, 2271-2294

Abstract: A single-server queue with renewal arrivals and generally distributed independent and identically distributed service times is considered. Customers are served using the longest remaining time first scheduling algorithm. In case of a tie, processor sharing is utilized. We introduce a fluid model for the evolution of a measure-valued state descriptor of this queue, and we investigate its properties. We also prove a fluid limit theorem justifying our fluid model as the first-order approximation of the queueing system under consideration.

Keywords: Primary: 60K25; secondary: 60F17; 68M12; 68M20; 90B22; 90B36; queueing; size-based protocols; longest remaining time first; measure-valued state descriptor; fluid model; fluid limit (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:4:p:2271-2294

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