2012/08/31 by Ke Han, Benedetto Piccoli, W.Y. Szeto +1 · 27 citations
Computer Science · Engineering · Mathematics · #Algebraic number #Conservation law #Kinematic wave #Kinematics #Network Traffic and Congestion Control #Numerical methods for differential equations #Property (philosophy) #Queue #Scalar (mathematics) #Shock wave #Traffic control and management #math.AP #msc:35B30 #msc:35C05 #msc:35L65
paper · pdf · doi:10.1080/21680566.2015.1064793
published in Transportmetrica B Transport Dynamics 4(3), 187-222 (Taylor & Francis) · 39 pages, 14 figures, 2 tables, Transportmetrica B: Transport Dynamics 2015
openalex publication_date 2015/08/18 · arxiv created 2016/03/27 · arxiv updated 2016/03/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.