A Random Walk Approach for Simulation-Based Continuous Dynamic Traffic Assignment

This paper presents a new simulation-based approach to address the stochastic Dynamic Traffic Assignment (DTA) problem, focusing on large congested networks and dynamic settings. The proposed methodology incorporates a random walk model inspired by the theoretical concept of the \textit{equivalent impedance} method, specifically designed to overcome the limitations of traditional Multinomial Logit (MNL) models in handling overlapping routes and scaling issues. By iteratively contracting non-overlapping subnetworks into virtual links and computing equivalent virtual travel costs, the route choice decision-making process is shifted to intersections, enabling a more accurate representation of travelers' choices as traffic conditions evolve and allowing more accurate performance under fine-grained temporal segmentation. The approach leverages Directed Acyclic Graphs (DAGs) structure to efficiently find all routes between two nodes, thus obviating the need for route enumeration, which is intractable in general networks. While with the calculation approach of downstream node choice probabilities, all available routes in the network can be selected with non-zero probability. To evaluate the effectiveness of the proposed method, experiments are conducted on two synthetic networks under congested demand scenarios using Simulation of Urban MObility (SUMO), an open-source microscopic traffic simulation software. The results demonstrate the method's robustness, faster convergence, and realistic trip distribution compared to traditional route assignment methods, making it an ideal proposal for real-time or resource-intensive applications such as microscopic demand calibration.