Efficient sensitivity analysis in dynamic continuum user-equilibrium models for urban cities

This study develops a sensitivity analysis framework for predictive dynamic continuum user-equilibrium (PDUE-C) models, which describe traffic evolution through a conservation law coupled with a time-dependent Hamilton–Jacobi equation. By differentiating the fully discrete numerical system, the proposed method directly computes gradients of traffic density and travel cost with respect to parameters in a Newell-type speed–density model. It avoids the perturbation errors and repeated equilibrium simulations associated with numerical differentiation, without requiring large matrix inversions. Numerical comparisons with finite differences verify the accuracy and stability of the computed sensitivities. The method is further incorporated into a bilevel topology-design problem, in which the sensitivity-based gradient algorithm converges more than five times faster than a derivative-free method. The results demonstrate the computational potential of discrete sensitivity analysis for coupled dynamic continuum traffic models and provide a methodological basis for applications to land-use evaluation and urban topology design.