Law of large numbers for the many-server earliest-deadline-first queue

TL;DR

This paper establishes a law of large numbers for a many-server queue operating under earliest deadline first discipline, using fluid models and measure-valued Skorohod maps to characterize the system's limiting behavior.

Contribution

It introduces a novel fluid model framework and proves the uniqueness and convergence of solutions for the many-server earliest-deadline-first queue.

Findings

Proves convergence of the queue to the fluid model solutions.

Establishes uniqueness of solutions to the fluid model equations.

Provides a mathematical characterization of the queue's limiting behavior.

Abstract

A many-server queue operating under the earliest deadline first discipline, where the distributions of service time and deadline are generic, is studied at the law of large numbers scale. Fluid model equations, formulated in terms of the many-server transport equation and the recently introduced measure-valued Skorohod map, are proposed as a means of characterizing the limit. The main results are the uniqueness of solutions to these equations, and the law of large numbers scale convergence to the solutions.