On the use of fixed point approximations to study reliable protocols over congested links

Analytical approaches for the performance investigation of portions of the Internet often consider the behavior of TCP over congested (or bottleneck) links. In several cases, the analysis is based on an iterative fixed point approximation (FPA) to compute the equilibrium point, in terms of packet loss rate and offered load, that represents the operating point of the network. Almost invariably, the FPA is conjectured to converge, but no proof of convergence is provided. This paper proves that a general model of a reliable protocol (such as TCP) over congested links converges to a unique stable solution under mild regularity conditions. This provides a justification of the convergence observed in the literature and a solid base for the further development of analytical approaches based on FPAs.