A model of TCP flows dynamics

The fluid-flow approximation models iuvestigate with much success the dynamics and stability of TCP/RED connections. Their main assumption is that the fluctuations of variables characterizing the behaviour of the couuectioiis are relatively small, that enables the linearization of model and the use of traditional control analysis tools to obtain such measures as Bode gain, phase margins, tracking error or delay margin. The coutribution of this article is twofold: (i) preserving linear fluid-flow model, we propose its extension to the case when a network is composed of wired and wireless part. In this case we consider a variant of TCP algorithiu (TCP-DCR) and fluid-flow differential equations representing the size of congestion window. mean queue at the bottleneck router and loss probability at a RED queue are supplemented with terms representing constant loss probability due to transmission in wireless pait and probability that a fraction of these errors is recovered by a liuk levei mechanism. The decrease of congestion window due to TCP mechanism is delayed to allow the link protocol to deal with the errors. The nonlinear model is linearized and may be used to check the stability of closed-loop control. (ii) We propose to replace the linear fluid flow model of the congested router queue and its AQM politias by more complex one, based on diffusiou approximation. The model will allow us to follow the queue evolution and its dynamics as well as the dynamics of congestion control, also when the transmission is far from the working point, including the case of saturated buffer. It might be especially useful when the counection dynamics is investigated in presence of large uncontrolled flows of UDP.