Reservoir-based surrogate modeling of dynamic user equilibrium

Abstract

This paper proposes a new dynamic user equilibrium (DUE) traffic assignment model using reservoir-based network reduction techniques and surrogate dynamic network loading models. A traffic network is decomposed into a reservoir structure, and the DUE problem is formulated as a variational inequality, with an embedded surrogate model for the path delay operator to describe traffic dynamics at the reservoir level. The surrogate model is further enhanced by the reproducing kernel Hilbert space and adaptive sampling to reduce approximation error and improve computational efficiency. To solve the proposed surrogate-based DUE problem on reduced networks, we develop a customized algorithm that integrates the kernel trick with the generalized projection framework. A pre-computation scheme is proposed, which calculates and stores the of kernel matrices and vectors, could further reduce the computational burden. Numerical experiments of the proposed methods show significant reduction of the computational times, by up to 90%, while maintaining low approximation errors (MAPE below 6%), when compared to the exact models and solution methods.