Fluid limits of G/G/1+G queues under the non-preemptive earliest-deadline-first discipline

Rami Atar, Anup Biswas, Haya Kaspi

Published 2013-05-12, updated 2014-08-20Version 2

A single-server queuing model is considered with customers that have deadlines. If a customer's deadline elapses before service is offered, the customer abandons the system (customers do not abandon while being served). When the server becomes available, it offers service to the customer having earliest deadline among those that are in the queue. We obtain a fluid limit of the queue length and abandonment processes and for the occupation measure of deadlines, in the form of measure-valued processes. We characterize the limit by means of a Skorohod problem in a time-varying domain, which has an explicit solution. The fluid limits also describe a certain process called the frontier, that is well known to play a key role in systems operating under this scheduling policy.