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

TL;DR

This paper derives fluid limit models for G/G/1+G queues with deadlines under a non-preemptive earliest-deadline-first discipline, characterizing queue dynamics and abandonment behavior through measure-valued processes.

Contribution

It introduces explicit fluid limit characterizations for queue length, abandonment, and deadline measures in a complex scheduling system, using a Skorohod problem framework.

Findings

Explicit fluid limit equations derived for queue length and abandonments.

Characterization of the frontier process in the fluid limit.

Solution of the Skorohod problem in a time-varying domain.

Abstract

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.