We focus on window flow control as used in packet-switched communication networks. The approach consists in studying the stability of a system where each node on the path followed by the packets of the controlled connection is modeled by a FIFO (First-In-First-Out) queue of infinite capacity which receives in addition some cross traffic represented by an exogenous flow. Under general stochastic assumptions, namely for stationary and ergodic input processes, we show the existence of a maximum throughput allowed by the flow control. Then we establish bounds on the value of this maximum throughput. These bounds which do not coincide in general, are reached by time-space scalings of the exogenous flows. Therefore, the performance of window flow control depends not only on the traffic intensity of the cross flows, but also on fine statistical characteristics such as the burstiness of these flows. These results are illustrated by several examples, including the case of a non-monotone, non-convex and fractal stability region.