  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.
