  For a class of large closed Jackson networks submitted to capacity
constraints, asymptotic independence of the nodes in normal traffic phase is
proved at stationarity under mild assumptions, using a Local Limit Theorem. The
limiting distributions of the queues are explicit. In the Statistical Mechanics
terminology, the equivalence of ensembles - canonical and grand canonical - is
proved for specific marginals. The framework includes the case of networks with
two types of nodes: single server/finite capacity nodes and infinite
servers/infinite capacity nodes, that can be taken as basic models for
bike-sharing systems. The effect of local saturation is modeled by generalized
blocking and rerouting procedures, under which the stationary state is proved
to have product-form. The grand canonical approximation can then be used for
adjusting the total number of bikes and the capacities of the stations to the
expected demand.
