A macroscopic dynamic network loading model for multiple-reservoir system

• Published in: Transportation research. Part B: methodological 2019-08, Vol.126, p.502-527
• Main Authors: Ge, Qian, Fukuda, Daisuke
• Format: Article
• Language: English
• Subjects: Differential equations; Dynamic network loading; Loads (forces); Macroscopic fundamental diagram; Mathematical models; Multiple-reservoir system; Numerical analysis; Numerical methods; Numerical scheme; Partial differential equations; Reservoirs; Traffic models
• ISSN: 0191-2615; 1879-2367
• DOI: 10.1016/j.trb.2018.06.008

•A dynamic network loading model is proposed using the macroscopic traffic variables.•The reservoir model is built on the conservation of flow in reservoir and the boundary model is built on the supply and demand of neighboring reservoirs.•The design parameters such as length and boundary of each internal path have been studied in depth.•This model is tested by several numerical experiments. In this paper, we present a dynamic network loading (DNL) model that captures the traffic dynamics for multiple-reservoir networks dependent on the relationship among macroscopic traffic characteristics, and develop a numerical method based on the Godunov scheme. The proposed DNL model consists of link model and node model. The traffic dynamics of the internal paths in a reservoir are specified by a system of Lighthill–Whitham–Richards-like partial differential equations, which build on the conservation law, while the flows at the boundaries between reservoirs are determined by the supply–demand balances between upstream and downstream reservoirs. A novel numerical method is developed based on the Godunov scheme to track the movement of vehicles in the network while maintaining the relevant priority rules. In comparison with previous approaches, the proposed numerical scheme is computationally efficient, considers the non-uniform cell sizes inherent in different internal paths within a reservoir, and conserves the flow through holding and balancing rules. Numerical experiments indicate that the proposed methodology can describe the dynamics of vehicles in large-scale traffic network efficiently.