动态流网络中的鲁棒分布式路由——第一部分：局部响应策略与弱弹性
Robust Distributed Routing in Dynamical Flow Networks - Part I: Locally Responsive Policies and Weak Resilience
AI总结：
研究动态流网络中分布式路由策略对抗链路流量容量恶意扰动的鲁棒性，提出一类仅依赖局部信息的分布式路由策略可实现最大弱弹性。
摘要：
针对降低链路流量容量的恶意扰动，研究了分布式路由策略在动态流网络中的鲁棒性。动态流网络被建模为基于有向无环图（具有单一源-目的地对和源处恒定流入）的质量守恒定律导出的常微分方程组。路由策略根据当前粒子密度，调节非目的地节点的流入在其出站链路间的分配方式，而链路的流出则通过流量函数依赖于该链路上的当前粒子密度。若目的地节点的总流入渐近地远离零，则称该动态流网络为部分传输的，其弱弹性被量化为使网络不再部分传输的所有扰动的最小链路幅度之和。结果表明，对于任意路由策略的动态流网络，弱弹性受限于网络的最小割容量，与初始流量条件无关。此外，一类仅依赖粒子密度局部信息并对此做出局部响应的分布式路由策略可实现该最大弱弹性。这些结果意味着路由策略可用信息的局部性约束不会导致弱弹性损失。详细分析了由局部响应分布式策略驱动的动态流网络的一些基本性质，包括全局收敛到唯一极限流。
英文摘要：
Robustness of distributed routing policies is studied for dynamical flow networks, with respect to adversarial disturbances that reduce the link flow capacities. A dynamical flow network is modeled as a system of ordinary differential equations derived from mass conservation laws on a directed acyclic graph with a single origin-destination pair and a constant inflow at the origin. Routing policies regulate the way the inflow at a non-destination node gets split among its outgoing links as a function of the current particle density, while the outflow of a link is modeled to depend on the current particle density on that link through a flow function. The dynamical flow network is called partially transferring if the total inflow at the destination node is asymptotically bounded away from zero, and its weak resilience is measured as the minimum sum of the link-wise magnitude of all disturbances that make it not partially transferring. The weak resilience of a dynamical flow network with arbitrary routing policy is shown to be upper-bounded by the network's min-cut capacity, independently of the initial flow conditions. Moreover, a class of distributed routing policies that rely exclusively on local information on the particle densities, and are locally responsive to that, is shown to yield such maximal weak resilience. These results imply that locality constraints on the information available to the routing policies do not cause loss of weak resilience. Some fundamental properties of dynamical flow networks driven by locally responsive distributed policies are analyzed in detail, including global convergence to a unique limit flow.
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