Heavy TraÆc Analysis for EDF Queues with Unbounded Lead Times

We present a heavy traÆc analysis for a G/G/1 queue in which customers have unbounded random deadlines correlated with their service times. The customers are processed according to the earliest-deadlinerst (EDF) queue discipline. At any time, the customers have a lead time, the time until their deadline lapses. We model the evolution of these lead times as a random measure on the real line. Under suitable scaling, it is proved that the measure-valued lead-time process converges to a deterministic function of the workload process. This work is a generalization of Doytchinov, Lehoczky and Shreve [6], which developed these results for the case of bounded deadlines independent of the service times. Another generalization of the latter results, covering the case of long range dependence, is also discussed.