Window flow control in FIFO networks with cross traffic

We focus on window flow control as used in packet-switched communication ne tworks. The approach consists in studying the stability of a system where e ach node on the path followed by the packets of the controlled connection i s modeled by a FIFO (First-In-First-Out) queue of infinite capacity which r eceives in addition some cross traffic represented by an exogenous flow. Un der general stochastic assumptions, namely for stationary and ergodic input processes, we show the existence of a maximum throughput allowed by the fl ow control. Then we establish bounds on the value of this maximum throughpu t. These bounds, which do not coincide in general, are reached by time-spac e scalings of the exogenous flows. Therefore, the performance of the 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 the se flows. These results are illustrated by several examples, including the case of a nonmonotone, nonconvex and fractal stability region.