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**Earliest-deadline-first service in heavy-traffic acyclic networks.**
*(English)*
Zbl 1084.60056

Summary: 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 B. Doytchinov, J. Lehoczky and S. Shreve [Ann. Appl. Probab. 11, 332–378 (2001; Zbl 1015.60086)], which developed these results for the single queue case.

### MSC:

60K25 | Queueing theory (aspects of probability theory) |

60G57 | Random measures |

60J65 | Brownian motion |

68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |

### Citations:

Zbl 1015.60086
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\textit{Ł. Kruk} et al., Ann. Appl. Probab. 14, No. 3, 1306--1352 (2004; Zbl 1084.60056)

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