基于改进Kelly算法拥塞控制策略的稳定性分析

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

针对网络中用户传播延时的不同,通过改进由Kelly等最初提出的离散控制策略,改变系统中的相关参数,引入最大-最小公平性概念建立对称Jacobian矩阵来证明系统在任意延时下是渐近稳定的,并给出了相应参数的取值范围.分析表明系统稳定性条件不受延时约束.数值例子说明系统收敛于平衡点的快速性也得到了保证.

To the different propagation delays between users in a network, a discrete congestion control scheme initially proposed by Kelly et af is used to improve it through changing the related parameters and introducing the concept of the max-rain 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.