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