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

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.