Abstract
Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment (DTA), 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, which is numerically implemented in a MATLAB package. In particular, the dynamic network loading (DNL) sub-problem is formulated as a system of differential algebraic equations based on the Lighthill-Whitham-Richards fluid dynamic model, which captures the formation, propagation and dissipation of physical queues as well as vehicle spillback on networks. Then, the fixed-point algorithm is employed to solve the DUE problems with simultaneous route and departure time choices 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 facilitate benchmarking a wide range of DUE algorithms and solutions, but also offer researchers a platform to further develop their own models and applications. The MATLAB package and computational examples are available at https://github.com/DrKeHan/DTA.
Highlights
This paper is concerned with a class of models known as dynamic user equilibrium (DUE)
DUE problems have been studied within the broader context of dynamic traffic assignment (DTA), which is viewed as the modeling of time-varying flows on traffic networks consistent with established travel demand and traffic flow theory
Both the dynamic network loading (DNL) procedure and the fixed-point algorithm are implemented in MATLAB, and Friesz et al (2011) Lo and Szeto (2002) Szeto and Lo (2004) Szeto and Lo (2006) Huang and Lam (2002) Tian et al (2012) Long et al (2013) Han et al (2015b) Han et al (2015a)
Summary
This paper is concerned with a class of models known as dynamic user equilibrium (DUE). The DNL model aims at describing and predicting the spatial and temporal evolution of traffic flows on a network that is consistent with established route and departure time choices of travelers This is done by introducing appropriate dynamics to flow propagation, flow conservation, link delay, and path delay on a network level. The effective delay operator is essential to the DUE model as it encapsulates the physics of the traffic network by capturing the dynamics of traffic flows at the link, junction, path, and network levels Where ‘a.e.’, standing for ‘for almost every’, is a technical term employed by measure-theoretic arguments to indicate that Eq (2.4) only needs to hold in [t0, tf ] with the exception of any subset that has zero Lebesgue measure
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
