This paper develops a sensitivity analysis framework for the perturbed utility route choice (PURC) model and the accompanying stochastic traffic equilibrium model. We derive analytical sensitivity expressions for the Jacobian of the individual optimal PURC flow and equilibrium link flows with respect to link cost parameters under general assumptions. This allows us to determine the marginal change in link flows following a marginal change in link costs across the network. We show how to implement these results while exploiting the sparsity generated by the PURC model. Numerical examples illustrate the use of our method for estimating equilibrium link flows after link cost shifts, identifying critical design parameters, and quantifying uncertainty in performance predictions. Finally, we demonstrate the method in a large-scale example. The findings have implications for network design, pricing strategies, and policy analysis in transportation planning and economics, providing a bridge between theoretical models and real-world applications.

翻译：本文针对扰动效用路径选择（PURC）模型及其伴随的随机交通均衡模型，构建了一个灵敏度分析框架。在一般假设条件下，我们推导了个体最优PURC流量和均衡路段流量关于路段成本参数的雅可比矩阵的解析灵敏度表达式。该框架能够确定路段成本发生边际变化时全网路段流量的边际变化量。我们展示了如何利用PURC模型产生的稀疏性来实现这些结果。数值算例验证了该方法在路段成本变化后均衡交通流量估计、关键设计参数识别以及性能预测不确定性量化中的应用。最后，我们在大规模算例中展示了该方法。研究成果对交通规划与经济中的网络设计、定价策略及政策分析具有启示意义，为理论模型与实际应用之间架起了桥梁。