标题： 具有级联失败的动态网络中的鲁棒分布式路由 显示英文标题

标题： Robust Distributed Routing in Dynamical Networks with Cascading Failures

摘要： 路由策略在网络中的鲁棒性是一个核心问题，随着对保护关键基础设施网络免受自然和人为破坏的认识增强，这个问题正受到越来越多的关注。在信息有限的情况下进行路由以及网络中可能出现级联效应，给这个问题带来了严峻的挑战。本摘要考虑了我们在先前工作中引入的动力网络框架[1,2]，其中网络通过一组常微分方程进行建模，这些方程来源于具有单一起点-终点对和起点恒定流入量的有向无环图的质量守恒定律。网络中每条链路上的粒子密度变化率等于该链路上的流入量与流出量之差。后者被建模为依赖于该链路上当前粒子密度的流量函数。本文的新建模元素是假设每条链路对于粒子密度具有有限容量，并且流量函数随着密度从零增加到最大密度容量而严格递增，在最大密度容量处是不连续的，此时流量函数值为零。这一特性特别允许了在我们的模型中出现溢流的可能性。在本文中，我们展示了在分布式路由下此类网络的弹性结果，针对那些减少链路流量函数的扰动。 显示英文摘要

摘要： Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited information and the possibility of cascades through the network adds serious challenges to this problem. This abstract considers the framework of dynamical networks introduced in our earlier work [1,2], where the network is modeled by a system of ordinary differential equations derived from mass conservation laws on directed acyclic graphs with a single origin-destination pair and a constant inflow at the origin. The rate of change of the particle density on each link of the network equals the difference between the inflow and the outflow on that link. The latter is modeled to depend on the current particle density on that link through a flow function. The novel modeling element in this paper is that every link is assumed to have finite capacity for particle density and that the flow function is modeled to be strictly increasing as density increases from zero up to the maximum density capacity, and is discontinuous at the maximum density capacity, with the flow function value being zero at that point. This feature, in particular, allows for the possibility of spill-backs in our model. In this paper, we present our results on resilience of such networks under distributed routing, towards perturbations that reduce link-wise flow functions.