Tails in generalized Jackson networks with subexponential service-time distributions
François Baccelli, Serguei Foss, and Marc Lelarge
Source: J. Appl. Probab. Volume 42, Number 2
(2005), 513-530.
Abstract
We give the exact asymptotics 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 taken to clear all customers present at some time t when stopping all arrivals that take place later than t.
We use the property that a large deviation of the maximal dater is caused by a single large service time at a single
station at some time in the distant past of t, in conjunction with fluid limits of generalized Jackson networks, to
derive the relevant asymptotics in closed form.
Secondary Subjects:
62G20
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1118777185
Digital Object Identifier: doi:10.1239/jap/1118777185
Mathematical Reviews number (MathSciNet): MR2145491
Zentralblatt MATH identifier: 1077.60067
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