INPUT-TO-STATE STABILITY IN CONGESTION CONTROL PROBLEM OF COMPUTER NETWORKS WITH NONLINEAR LINKS

作者：Moarefianpour Ali; Majd Vahid Johari^*

来源：International Journal of Innovative Computing Information and Control, 2009, 5(8): 2091-2105.

• Congestion control
• Computer networks
• Input-to-state stability
• Nonlinear dynamics
• Primal-dual algorithm

In this paper, we address the stability of congestion control in Internet, considering all unmodeled flows as exogenous disturbances. In contrast with previous works, we suppose that both sets of senders and links in the network have nonlinear dynamics, and model the network based on fluid flow approximation. Each sender updates its sending rate to minimize its own cost function. The sending rate dynamics of each sender consist of a linear and a nonlinear subsystem in cascade form. The linear subsystem acts as dynamical pricing filter to improve the transients of the network congestion problem. For the obtained primal-dual algorithm, we first derive the existence conditions of the equilibrium point of the closed loop system; then we prove that the proposed control law guarantees input-to-state stability (ISS). The obtained general results are further simplified for two types of typical filters, namely, proportional and proportional plus approximate derivative filters. Using network simulator ns-2, we verify the performance of the proposed congestion control law for some network topologies.

• 出版日期2009-8