Earliest-deadline-first service in heavy-traffic acyclic networks

Details Earliest-deadline-first service in heavy-traffic acyclic networks Earliest-deadline-first service in heavy-traffic acyclic networks

2004-07-08

arxiv.org/abs/math/0407136v1

Annals of Probability 2004, Vol. 14, No. 3, 1306-1352

Mathematics

Probability

Scientific paper

10.1214/105051604000000314

This paper presents a heavy traffic analysis of the behavior of multi-class acyclic queueing networks in which the customers have deadlines. We assume the queueing system consists of J stations, and there are K different customer classes. Customers from each class arrive to the network according to independent renewal processes. The customers from each class are assigned a random deadline drawn from a deadline distribution associated with that class and they move from station to station according to a fixed acyclic route. The customers at a given node are processed according to the earliest-deadline-first (EDF) queue discipline. At any time, the customers of each type at each node have a lead time, the time until their deadline lapses. We model these lead times as a random counting measure on the real line. Under heavy traffic conditions and suitable scaling, it is proved that the measure-valued lead-time process converges to a deterministic function of the workload process.

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