## The Annals of Applied Probability

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

#### Abstract

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. A two-station example is worked out in detail, and simulation results are presented to illustrate the predictive value of the theory. This work is a generalization of Doytchinov, Lehoczky and Shreve [Ann. Appl. Probab. 11 (2001) 332–379], which developed these results for the single queue case.

#### Article information

Source
Ann. Appl. Probab., Volume 14, Number 3 (2004), 1306-1352.

Dates
First available in Project Euclid: 13 July 2004

https://projecteuclid.org/euclid.aoap/1089736287

Digital Object Identifier
doi:10.1214/105051604000000314

Mathematical Reviews number (MathSciNet)
MR2071425

Zentralblatt MATH identifier
1084.60056

#### Citation

Kruk, Łukasz; Lehoczky, John; Shreve, Steven; Yeung, Shu-Ngai. Earliest-deadline-first service in heavy-traffic acyclic networks. Ann. Appl. Probab. 14 (2004), no. 3, 1306--1352. doi:10.1214/105051604000000314. https://projecteuclid.org/euclid.aoap/1089736287

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