Thermodynamic Limit and Propagation of Chaos in Polling Networks
Abstract
{${\P\n,¸N\geq 1 }$ is a sequence of standard polling networks, consisting of $N$ nodes attended by $V\n$ mobile servers. When a server arrives at a node $i$, he serves one of the waiting customers, if any, and then moves to node $j$ with probability $p_{ij}\n$. Customers arrive according to a Poisson process. Service requirements and switch-over times between nodes are independent exponentially distributed random variables. The behavior of $\P\n$ is analyzed in {\em thermodynamic limit}, i.e when both $N$ and $V\n$ tend to infinity, with $U\egaldef\lim_{N\rightarrow\infty}V\n/N,\ 0