FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 4, PAGES 1259-1266

**Limit theorems for asymmetric transportation networks**

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 $$**R**^{a}.
We prove that $U$_{N}(t) converges
in distribution to a non-linear dynamical system $$**g** → **u**(t,**g**)
(assuming convergence of initial distributions
$U$_{N}(0) → **g**),
where $$**g**
Î
**R**^{a}.
The dynamical system has the only invariant measure to which the
invariant measures of processes $U$_{N}(t) converge
as $N\; \to $¥.

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Last modified: April 17, 2002