TY - JOUR
T1 - The variational formulation of a non-equilibrium traffic flow model
T2 - Theory and implications
AU - Li, Jia
AU - Zhang, H. M.
PY - 2013/11
Y1 - 2013/11
N2 - The analysis and numerical solution of non-equilibrium traffic flow models in current literature are almost exclusively carried out in the hyperbolic conservation law framework, which requires a good understanding of the delicate and non-trivial Riemann problems for conservation laws. In this paper, we present a novel formulation of certain non-equilibrium traffic flow models based on their isomorphic relation with optimal control problems. This formulation extends the minimum principle observed by the LWR model. We demonstrate that with the new formulation, generic initial-boundary conditions can be conveniently handled and a simplified numerical solution scheme for non-equilibrium models can be devised. Besides deriving the variational formulation, we provide a comprehensive discussion on its mathematical properties and physical implications.
AB - The analysis and numerical solution of non-equilibrium traffic flow models in current literature are almost exclusively carried out in the hyperbolic conservation law framework, which requires a good understanding of the delicate and non-trivial Riemann problems for conservation laws. In this paper, we present a novel formulation of certain non-equilibrium traffic flow models based on their isomorphic relation with optimal control problems. This formulation extends the minimum principle observed by the LWR model. We demonstrate that with the new formulation, generic initial-boundary conditions can be conveniently handled and a simplified numerical solution scheme for non-equilibrium models can be devised. Besides deriving the variational formulation, we provide a comprehensive discussion on its mathematical properties and physical implications.
KW - Hamilton-Jacobi equations
KW - Kinematic wave
KW - Non-equilibrium traffic models
KW - Variational formulation
UR - http://www.scopus.com/inward/record.url?scp=85027938780&partnerID=8YFLogxK
U2 - 10.1016/j.trb.2013.06.005
DO - 10.1016/j.trb.2013.06.005
M3 - Article
AN - SCOPUS:85027938780
SN - 0191-2615
VL - 57
SP - 314
EP - 325
JO - Transportation Research Part B: Methodological
JF - Transportation Research Part B: Methodological
ER -