Boundedness and Global Stability of a Nonlinear Congestion Control With Delays
Boundedness and Global Stability of a Nonlinear Congestion Control With Delays
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DOI：
10.1109/tac.2006.880794
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发表时间：
2006-09
影响因子：
6.8
通讯作者：
Zhikui Wang;F. Paganini
中科院分区：
文献类型：
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作者：
Zhikui Wang;F. Paganini
本文研究了一类具有时滞的“对偶”非线性拥塞控制的全局动力学问题。结果表明，对于任意时延、容量和拓扑结构的网络，这种控制律能够在其唯一平衡点附近保持局部动态稳定性。我们在这里关注的是单一瓶颈网络的情况，由具有异构延迟的流量源共享。我们首先证明，对于任何参数值，在一定时间后的系统状态都可以给出一个先验界。其次，证明了时滞微分方程在增益参数和时滞约束下的全局指数稳定性；这些条件比线性稳定性条件更有限制性，但在齐次延迟情况下限制性较弱。该证明是基于对系统轨迹的详细研究和边界
This note concerns the global dynamics of a "dual" nonlinear congestion control with time-delays. It has been shown that such control laws are able to maintain local dynamic stability around their unique equilibrium point for networks of arbitrary delay, capacity and topology. We focus here on the case of a single bottleneck network, shared by traffic sources with heterogeneous delays. We first prove that, for any parameter values, an a priori bound can be given on the system state after a certain amount of time. Next, we prove global exponential stability of the delay-differential equations under constraints on its gain parameter and the delays; these are more restrictive than conditions for linear stability, but only mildly so in the homogeneous delay case. The proof is based on a detailed investigation and bounding of the system trajectories