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Numerical Analysis and Scientific Computingmathscidoc:1610.25051

Transportation Research Part B, 56, 96-119, 2013
Jiang et al. (Transportation Research Part B, 2011, 45(2), 343-363) proposed a predictive continuum dynamic user-optimal (PDUO-C) model to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers. The modeled region is a dense urban city, which is arbitrary in shape and has a single central business district (CBD). However, we argue that the model is not well posed due to an inconsistency in the route-choice strategy. To overcome this inconsistency, we revisit the PDUO-C problem, and construct an improved path-choice strategy. The improved model consists of a conservation law to govern the density, in which the flow direction is determined by the improved path-choice strategy, and a Hamilton-Jacobi equation to compute the total travel cost. The simultaneous satisfaction of both equations can be treated as a fixed-point problem. A self-adaptive method of successive averages (MSA) is proposed to solve this fixed-point problem. This method can automatically determine the optimal MSA step size using the least squares approach. Numerical examples are used to demonstrate the effectiveness of the model and the solution algorithm.
Continuum model, Dynamic traffic assignment, Predictive user equilibrium, Path-choice strategy, Conservation law, Hamilton-Jacobi equation, Fixed-point problem, Method of successive averages (MSA), Self-adaptive
```@inproceedings{jie2013revisiting,
title={ Revisiting Jiang's dynamic continuum model for urban cities},
author={Jie Du, S.C. Wong, Chi-Wang Shu, Tao Xiong, Mengping Zhang, and Keechoo Choi},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012053015581177169},
booktitle={Transportation Research Part B},
volume={56},
pages={96-119},
year={2013},
}
```
Jie Du, S.C. Wong, Chi-Wang Shu, Tao Xiong, Mengping Zhang, and Keechoo Choi. Revisiting Jiang's dynamic continuum model for urban cities. 2013. Vol. 56. In Transportation Research Part B. pp.96-119. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012053015581177169.