Source: J. Appl. Probab. Volume 42, Number 2
(2005), 491-512.
We use a sample-path technique to derive asymptotics of
generalized Jackson queueing networks in the fluid scale; that is,
when space and time are scaled by the same factor n. The
analysis only presupposes the existence of long-run averages and
is based on some monotonicity and concavity arguments for the
fluid processes. The results provide a functional strong law of
large numbers for stochastic Jackson queueing networks, since they
apply to their sample paths with probability 1. The fluid
processes are shown to be piecewise linear and an explicit
formulation of the different drifts is computed. A few
applications of this fluid limit are given. In particular, a new
computation of the constant that appears in the stability
condition for such networks is given. In a certain context of a
rare event, the fluid limit of the network is also derived
explicitly.
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