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Publication 05-CNA-16
Heavy Traffic Analysis for EDF Queues with Unbounded Lead Times August 12, 2005 Lukasz Kruk
Abstract: We present a heavy traffic analysis for
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queue in which customers have unbounded random deadlines
correlated with their service times. The customers are processed
according to th earliest-deadline-first (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.