Geodesic
Limit theorems for asymmetric transportation networks
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1259-1266.

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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 $N\to\infty$. 
@article{FPM_2001_7_4_a16,
     author = {D. V. Khmelev},
     title = {Limit theorems for asymmetric transportation networks},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1259--1266},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a16/}
}
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D. V. Khmelev. Limit theorems for asymmetric transportation networks. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1259-1266. http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a16/