FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 4, PAGES 1259-1266
D. V. Khmelev
Abstract
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We consider a model of an asymmetric transportation network.
The transportation network is described by the Markov
process $U_N(t)$ . This process has values in a compact subset of
the finite-dimensional real vector space $\mathbb R^{\alpha}$ .
We prove that $U_N(t)$ converges in distribution to
a non-linear dynamical system $\mathbf g\to \mathbf u(t,\mathbf g)$
(assuming convergence of initial distributions
$U_N(0)\to \mathbf g$ ), where $\mathbf g\in\mathbb R^{\alpha}$ .
The dynamical system has the only invariant measure to which
the invariant measures of processes $U_N(t)$ converge as $N\to\infty$ .
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Last modified: April 17, 2002