扰动效用随机交通均衡的灵敏度分析
Sensitivity analysis of the perturbed utility stochastic traffic equilibrium
AI总结：
本文提出针对扰动效用路径选择模型的灵敏度分析框架，推导了链流对链成本参数的雅可比表达式，通过稀疏性实现结果应用，展示了方法在估计均衡链流、识别关键参数及量化不确定性方面的价值。
摘要：
本文发展了一种针对扰动效用路径选择（PURC）模型及其伴随随机交通均衡模型的灵敏度分析框架。我们推导了在一般假设下，个体最优PURC流量和均衡链流对链成本参数的雅可比灵敏度表达式。这使我们能够确定在网络中链成本的边际变化对链流的边际变化。我们展示了如何利用PURC模型生成的稀疏性来实施这些结果。数值示例展示了我们方法在估计链成本变化后的均衡链流、识别关键设计参数以及量化性能预测的不确定性方面的应用。最后，我们在一个大规模示例中展示了该方法。这些发现对交通规划和经济学中的网络设计、定价策略和政策分析具有启示，为理论模型与现实应用之间架起了桥梁。
英文摘要：
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.
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