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模型及其伴随的随机交通均衡模型，构建了一个敏感性分析框架。我们在一般性假设下，推导了关于路段成本参数的个体最优扰动效用路径选择流量与均衡路段流量的雅可比矩阵的解析敏感性表达式。这使得我们能够确定网络中路段成本发生边际变化时，路段流量的边际变化。我们展示了如何在利用扰动效用路径选择模型生成的稀疏性的同时，实现这些结果。数值算例说明了我们的方法在估计路段成本变化后的均衡路段流量、识别关键设计参数以及量化性能预测不确定性方面的应用。最后，我们通过一个大规模算例展示了该方法。研究结果对交通规划与经济学中的网络设计、定价策略和政策分析具有启示意义，为理论模型与现实应用之间搭建了桥梁。