Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness
Abstract
We present a continuous-time link-based kinematic wave model (LKWM) for dynamic traffic networks based on the scalar conservation law model. Derivation of the LKWM involves the variational principle for the Hamilton-Jacobi equation and junction models defined via the notions of demand and supply. We show that the proposed LKWM can be formulated as a system of differential algebraic equations (DAEs), which captures shock formation and propagation, as well as queue spillback. The DAE system, as we show in this paper, is the continuous-time counterpart of the link transmission model. In addition, we present a solution existence theory for the continuous-time network model and investigate continuous dependence of the solution on the initial data, a property known as well-posedness. We test the DAE system extensively on several small and large networks and demonstrate its numerical efficiency.
Cite
@article{arxiv.1208.5141,
title = {Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness},
author = {Ke Han and Benedetto Piccoli and W. Y. Szeto},
journal= {arXiv preprint arXiv:1208.5141},
year = {2016}
}
Comments
39 pages, 14 figures, 2 tables, Transportmetrica B: Transport Dynamics 2015