Stability Analysis of a Congestion Control Scheme Based on Improved Kelly Algorithm

To the different propagation delays between users in a network,a discrete congestion control scheme initially proposed by Kelly et al is used to improve it through changing the related parameters and introducing the concept of the max-min fairness into it to build a symmetric Jacobian matrix so as to prove that the system is asymptotically stable to any delay,with the range of the corresponding parameters given for valuation.The analysis results showed that the stability condition of the system is therefore unconstrained by any delay.Numerical examples revealed that the system is ensured to converge fast at the equilibrium point.