Exact and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model with bounded acceleration for a class of fundamental diagrams
KAUST DepartmentMechanical Engineering Program
Electrical Engineering Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Distributed Sensing Systems Laboratory (DSS)
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AbstractIn this article, we propose a new exact and grid-free numerical scheme for computing solutions associated with an hybrid traffic flow model based on the Lighthill-Whitham-Richards (LWR) partial differential equation, for a class of fundamental diagrams. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a constant acceleration otherwise. We first propose a mathematical definition of the solution as a minimization problem. We use this formulation to build a grid-free solution method for this model based on the minimization of component function. We then derive these component functions analytically for triangular fundamental diagrams, which are commonly used to model traffic flow. We also show that the proposed computational method can handle fixed or moving bottlenecks. A toolbox implementation of the resulting algorithm is briefly discussed, and posted at https://dl.dropbox.com/u/1318701/Toolbox.zip. © 2013 Elsevier Ltd.
SponsorsThe authors are indebted to Jean-Baptiste Lesort for fruitful conversations regarding vehicular models and traffic flow coupling. The authors would also like to thank Ludovic Leclercq and Jean-Patrick Lebacque for fruitful conversations regarding the two-phase traffic flow model, well before this article was written. The development of a preliminary version of the algorithm presented in this article was supported both by INRETS (currently IFSTTAR), France, as well as UC Berkeley, USA.