Network link flow data are an intuitive information for monitoring the traffic condition of the entire network, and can be used to enhance traffic management and control. Link flow observation systems are typically designed using flow conservation equations to obtain the information of flow on unobserved links by inference. The occurrence of sensor failures in such systems may lead to flow information loss on both observed and inferred links. Most studies on this issue have considered sensor deployment and failure evaluation as separate processes. In contrast, in this study, both processes are integrated to establish a link flow observation system that withstands sensor failures. First, we propose a novel model to solve the sensor location problem for full link flow observability. The proposed model is then modified to evaluate the link flow information loss in sensor failure event, and incorporated into a distributionally robust optimization (DRO) model for the sensor location problem concerned. The DRO model minimizes the worst-case expected information loss of the system during the planning horizon with different types of sensors. Moreover, we extend the DRO model to a target-based version, into which a convex risk measure named Observation fulfillment risk index is introduced to evaluate the risk of failing to meet the predetermined observation target for any sensor installation schemes. The devised models can be directly solved by commercial solvers for networks like Nguyen–Dupuis, and a matheuristic genetic algorithm is designed for large-scale example networks. Numerical experiments are performed for networks with different sizes. The DRO model generates robust sensor location schemes with worst-case performances that are superior to those achieved using benchmark methods, such as stochastic programming. The use of the Observation fulfillment risk index enhances the system stability and target fulfillment level and decreases the standard deviation of the link flow information loss. We also make use of numerical experiments to derive some insightful conclusions on installation budget, coverage ratio, failure risks, etc.

网络链路流量数据是监控整个网络流量状况的直观信息，可用于加强流量管理和控制。链路流量观测系统通常使用流量守恒方程来设计，通过推理获得未观测链路上的流量信息。此类系统中传感器故障的发生可能会导致观察到的和推断的链路上的流信息丢失。关于这个问题的大多数研究都将传感器部署和故障评估视为单独的过程。相比之下，在本研究中，这两个过程被集成以建立一个能够承受传感器故障的链路流观测系统。首先，我们提出了一种新颖的模型来解决全链路流可观测性的传感器定位问题。然后修改所提出的模型以评估传感器故障事件中的链路流信息丢失，并将其纳入相关传感器位置问题的分布式鲁棒优化（DRO）模型中。DRO 模型使用不同类型的传感器，在规划范围内最大限度地减少系统最坏情况下的预期信息丢失。此外，我们将DRO模型扩展到基于目标的版本，其中引入了称为观测履行风险指数的凸风险度量来评估任何传感器安装方案未能满足预定观测目标的风险。设计的模型可以直接由 Nguyen-Dupuis 等网络的商业求解器求解，并且数学遗传算法是为大规模示例网络设计的。对不同规模的网络进行了数值实验。DRO 模型生成稳健的传感器定位方案，其最坏情况下的性能优于使用基准方法（例如随机编程）实现的方案。观测履约风险指数的使用，提高了系统的稳定性和目标履约水平，降低了链路流信息损失的标准差。我们还利用数值实验得出有关安装预算、覆盖率、故障风险等的一些富有洞察力的结论。