The last, the least, and the urgent: Fluid modeling and performance equivalence for scheduling policies in partial service queues with abandonment

In several queueing systems, arriving tasks have both service and timing requirements, and depart whenever one of them is attained. In several applications, the partial work performed by the system on tasks during their stay is still useful, even if the task is not completed. We analyze these partial service queues with abandonment under a many-server setting and characterize the equilibrium performance of several policies through fluid models. In particular, we show that deadline-oblivious policies like Least-Attained-Service and Last-Come-First-Served exhibit the same equilibrium performance as Earliest-Deadline-First. This striking property means that designers may avoid the difficult job of estimating deadlines without performance penalties. The conclusions are validated by numerical experiments.