Are optimization based Internet congestion control models fragile with respect to TCP structure and symmetry?

Scalable stability conditions derived so far for optimization based models of congestion control protocols, can be shown mathematically to hold for arbitrary networks provided the underlying protocol is symmetric. In practical implementations, however, deviation from this symmetry is inevitable. It is hence crucial to establish whether these models are fragile with respect to a relaxation of the symmetry assumption. We prove in this paper that this is not the case by presenting scalable, decentralized conditions, that guarantee stability for models of non-symmetric, TCP like protocols, of arbitrary interconnection. These conditions can be seen as local perturbations to the symmetric results and we illustrate how they converge to those derived for symmetric protocols as the degree of non symmetry becomes smaller. Finally, we show the way the decrease rule in TCP is associated with robust stability to non symmetric deviations from the protocol.