一类网络速率控制和路由联合算法的稳定性

Stability of a Joint Rate Control and Routing Scheme in Networks

近年来,动态多路径路由下网络速率控制的研究受到广泛关注.本文提出了一个新的速率控制和多路径路由联合的算法,该算法的特点是具有唯一的平衡点.利用传统的Lyapunov方法,我们证明算法在没有传播时延情形下的全局稳定性.而且,更为重要的是,即使考虑传播时延,在一定的条件下,该算法是局部稳定的.在平衡点处,每条路由上的速率非零.这一事实不但去掉了Kelly F P,Voice T(2005)结果中内部平衡点的假设条件,而且也可以理解为一种探测机制.我们通过仿真证实了算法的正确性,同时仿真结果也表明局部稳定性的吸引域可以很大,甚至是全局稳定的.

Recently, rate control in networks with dynamic multi-path routing has been more and more widely concerned. In this paper, we propose a new joint rate control and routing scheme, and then analyze its stability under a flnid-flow model. This scheme has a unique equilibrium point. This paper, like most, presents a global stability in the absence of propagation delays by using conventional Lyapunov method. What＇s more, we find a sufficient condition for local stability in the presence of propagation delays. At an equilibrium point, the transmission rate on each path is nonzero, which not only removes the assumption of interior equilibrium points once named by Kelly F P and Voice T （2005） in their previous work, but also allows us to interpret it as a probing protocol. We also show through simulation that this algorithm seems to ensure global stability or, at least, ensure convergence from a large region of attraction around the equilibrium point with heterogeneous delays.