  We are interested in analyzing the effect of bandwidth sharing for
telecommunication networks. More precisely, we want to calculate which routes
are bottlenecks by means of large deviations techniques. The method is
illustrated in this paper on a star network, where the bandwidth is shared
between customers according to the so-called min policy. We prove a sample path
large deviation principle for a rescaled process n^{-1}Q_{nt}, where Q_t
represents the joint number of connections at time t. The main result is to
compute the rate function explicitly. The major step consists in deriving large
deviation bounds for an empirical generator constructed from the join number of
customers and arrivals on each route. The rest of the analysis relies on a
suitable change of measure together with a localization procedure. An example
shows how this can be used practically.
