Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation

Abstract

Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment, in which road travelers engage in a non-cooperative Nash-like game with departure time and route choices. DUE models describe and predict the time-varying traffic flows on a network consistent with traffic flow theory and travel behavior. This paper documents theoretical and numerical advances in synthesizing traffic flow theory and DUE modeling, by presenting a holistic computational theory of DUE with numerical implementation encapsulated in a MATLAB software package. In particular, the dynamic network loading (DNL) sub-problem is formulated as a system of differential algebraic equations based on the fluid dynamic model, which captures the formation, propagation and dissipation of physical queues as well as vehicle spillback on networks. Then, the fixedpoint algorithm is employed to solve the DUE problems on several large-scale networks. We make openly available the MATLAB package, which can be used to solve DUE problems on user-defined networks, aiming to not only help DTA modelers with benchmarking a wide range of DUE algorithms and solutions, but also offer researchers a platform to further develop their own models and applications. Updates of the package and computational examples are available at https://github.com/DrKeHan/DTA.

Cross‐comparison of convergence algorithms to solve trip‐based dynamic traffic assignment problems

“…Note that is determined in the light of the recent study of Han, Eve, and Friesz (2018) in which this algorithm is applied to a flow-based DTA problem. At every iteration, the algorithm attempts to swap users from the path with longer travel time compared to mean travel time to the shortest path and other low-cost paths.…”

“…At every iteration, the algorithm attempts to swap users from the path with longer travel time compared to mean travel time to the shortest path and other low-cost paths. Note that is determined in the light of the recent study of Han, Eve, and Friesz (2018) in which this algorithm is applied to a flow-based DTA problem. Note that in Equation (18), we can have a negative number for swapping, meaning that users should be added to this path.…”

Simulation‐based dynamic traffic assignment: Meta‐heuristic solution methods with parallel computing

“…To evaluate the performance of the solution methods in the absence of the path discovery procedure, we fixed the path set for all ODs and rerun the optimization algorithms. In other words, the optimization is started from a predefined set of paths, which is also an option for simulation-based DTA (Han, Eve, & Friesz, 2019). It means there is no outer loop in the optimization process, and we directly iterate in the inner loop for each assignment period.…”

Day-to-day dynamic traffic assignment with imperfect information, bounded rationality and information sharing

“…In this paper, we employ the variational formulation of the Lighthill-Whitham-Richards model known as the Lax-Hopf formula , and the DNL model formulated as a system of differential algebraic equations. For space limitation, we outline the main steps of the DNL and refer the reader to Han et al (2018) for further derivation and details.…”

“…The LWR-based DNL procedure is formulated as a system of differential algebraic equations, and we present its discretized version here without going through the detailed derivation. For more extensive discussion and numerical examples, the reader is referred to Han et al (2018). Recalling the notations from Section 4.1, we present the DNL procedure in discrete time as follows.…”