On the Stability of Primal-Dual Congestion Control Algorithm in the Presence of Exogenous Disturbances

In this paper, we consider the effects of exogenous disturbances on the closed-loop system of the congestion control problem in a network with general structure. This investigation is important since many of data flows in internet network are considered as unmodeled flows. In contrast to previous works, we suppose that both senders and links in the network have dynamics. Each sender updates its sending rate to minimize its own cost function. The network is modeled based on fluid flow approximation with nonlinear dynamics for the links. In this research, we first derive the conditions for the existence of the system equilibrium point taking into account the constraint sets of the problem. Then, we prove input-to-state stability (ISS) of the closed-loop system for the congestion control problem with input and output disturbances in the network links. We further show that the obtain results are valid even when the routing matrix of the network varies. Finally, we verify the theoretical results by simulation on two different multi-link networks.