Solution to static traffic assignment problem with shock structures on a single origin-destination parallel road network
Speaker:
Prof. Peng Zhang
School of Mechanics and Engineering Sciences
Shanghai University, China
Date: May 12, 2026 (Tuesday)
Time: 5:00 pm – 6:00 pm
Venue: Room 612B, 6/F Haking Wong Building, The University of Hong Kong
Language: Putonghua
Abstract
It mathematically indicates that shock structures are essential in static traffic assignment (STA) problems. The study is based upon the Lighthill-Witham-Richards (LWR) model or the theory of fundamental diagram, and takes a single origin-destination (OD) parallel road network as an instance, in which the user-equilibrium condition is satisfied. Taking the total number of users on the network as the independent variable, it shows that there are no classical steady-state solutions to the problem for the number between two critical values, thus shock structures must be introduced to complete the solution in the interval. Dynamic simulation of the LWR model on two ring networks is implemented to show that casually distributed traffic flow converges to analytical solutions, corresponding to the user number on the ring network. However, extensions of this study to more complex road networks are still challenging. For more details, see Z. Lin, P. Zhang, et al, Transportmetrica B: Transport Dynamics, 2024, vol.12, No.1, 2341012; Lyu, Y.P., Steady-State Solution on a Simple Single Origin-Destination Road Network based on LWR Model and User-Equilibrium Conditions, Dissertation, Shanghai University, 2022.
About the speaker
Professor Peng Zhang has a bachelor's degree in Mathematics from Sichuan University, a PhD and DSc in Mathematics from the University of Science and Technology of China. He is now a full professor at School of Mechanics and Engineering Sciences, Shanghai University, China. Professor Zhang has an educational and research background in the computational theory of hyperbolic conservation laws, and he focuses on traffic flow problems using the theory. His contribution to traffic flow problems mainly involves the mathematical theory, which includes the analytical properties in (1) the higher-order model; (2) the multi-class model; and (3) the models with discontinuous fluxes or inhomogeneous road conditions. Since 2003, he has published more than 50 SCI papers on such reputed Journals as J. Comput. Phys., Euro. J. Appl. Math., Numer. Meth. Partial Diff. Equ., SIAM J. Appl. Math., Appl. Numer. Math., J Comput. Appl. Math., Phys. Rev. E, Trans. Res. Part B, etc.
