On the stable behaviors of window flow control

We focus on window flow control in loss-less packet-switched networks. In our model, the window is static and all packets of the controlled connection follow the same path through the network. Each router on this path processes packets of other connections, which we refer to as exogenous traffic. The stochastic assumptions are quite general, since the input processes are only assumed to be stationary and ergodic. We study the stability region of the model, i.e. the conditions on the arrival rates and the service rates of the controlled and the exogenous flows, under which there exists a finite stationary regime. In particular, we obtain bounds on the maximal throughput of the connection allowed by the flow control.