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Tails in Generalized Jackson Networks with Subexponential Service Distributions

François Baccelli 1 Serguei Foss Marc Lelarge 1
1 TREC - Theory of networks and communications
DI-ENS - Département d'informatique - ENS Paris, Inria Paris-Rocquencourt
Abstract : We give the exact asymptotic of the tail of the stationary maximal dater in generalized Jackson networks with subexponential service times. This maximal dater, which is an analogue of the workload in an isolated queue, gives the time to clear all customers present at some time t when stopping all arrivals taking place later than t. We use the property that a large deviation of the maximal dater is caused by a single large service time in a single station at some distant time in the past of t and fluid limits of generalized Jackson networks to derive the asymptotic in question in closed form.
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https://hal.inria.fr/inria-00071502
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Submitted on : Tuesday, May 23, 2006 - 5:47:23 PM
Last modification on : Thursday, March 17, 2022 - 10:08:32 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:20:08 PM

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François Baccelli, Serguei Foss, Marc Lelarge. Tails in Generalized Jackson Networks with Subexponential Service Distributions. [Research Report] RR-5081, INRIA. 2004. ⟨inria-00071502⟩

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