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Date: 06/99
Title: Mean-field approximation for stochastic transportation network and stability of dynamical system

Authors: D.V. Khmelev and V.I. Oseledets


Abstract:
A queuing system is considered, with a virtual node, $N$ nodes, and
$rN$ servers. At each node (of these $N$ nodes) the arrivals of particles
form a Poisson flow of rate $\lambda(t)$. For an empty node a particle
leaves the system. A server at the node takes the particle and moves to a
random node. Travelling time is exponential of mean $1$. The number of
servers at each node (of these $N$ nodes) is bounded by $m$.

We discuss the property of stability for the
limiting deterministic process as $N\to\infty$.
Furthermore, we consider a particular queuing system with
dynamical routing.