TY - JOUR
T1 - Reformulating the Hoogendoorn-Bovy predictive dynamic user-optimal model in continuum space with anisotropic condition
AU - Du, Jie
AU - Wong, S. C.
AU - Shu, Chi Wang
AU - Zhang, Mengping
N1 - Publisher Copyright:
© 2015 Elsevier Ltd.
PY - 2015/9/1
Y1 - 2015/9/1
N2 - Hoogendoorn and Bovy (2004) developed an approach for a pedestrian user-optimal dynamic assignment in continuous time and space. Although their model was proposed for pedestrian traffic, it can also be applied to urban cities. The model is very general, and consists of a conservation law (CL) and a Hamilton-Jacobi-Bellman (HJB) equation that contains a minimum value problem. However, only an isotropic application example was given in their paper. We claim that the HJB equation is difficult to compute numerically in an anisotropic case. To overcome this, we reformulate their model for a dense urban city that is arbitrary in shape and has multiple central business districts (CBDs). In our model, the minimum value problem is only used in the CL portion, and the HJB equation reduces to a Hamilton-Jacobi (HJ) equation for easier computation. The dynamic path equilibrium of our model is proven in a different way from theirs, and a numerical algorithm is also provided to solve the model. Finally, we show two numerical examples under the anisotropic case and compare the results with those of the isotropic case.
AB - Hoogendoorn and Bovy (2004) developed an approach for a pedestrian user-optimal dynamic assignment in continuous time and space. Although their model was proposed for pedestrian traffic, it can also be applied to urban cities. The model is very general, and consists of a conservation law (CL) and a Hamilton-Jacobi-Bellman (HJB) equation that contains a minimum value problem. However, only an isotropic application example was given in their paper. We claim that the HJB equation is difficult to compute numerically in an anisotropic case. To overcome this, we reformulate their model for a dense urban city that is arbitrary in shape and has multiple central business districts (CBDs). In our model, the minimum value problem is only used in the CL portion, and the HJB equation reduces to a Hamilton-Jacobi (HJ) equation for easier computation. The dynamic path equilibrium of our model is proven in a different way from theirs, and a numerical algorithm is also provided to solve the model. Finally, we show two numerical examples under the anisotropic case and compare the results with those of the isotropic case.
KW - Anisotropic
KW - Conservation law
KW - Continuum model
KW - Dynamic traffic assignment
KW - Hamilton-Jacobi equation
KW - Predictive user equilibrium
UR - https://www.scopus.com/pages/publications/84933039055
U2 - 10.1016/j.trb.2015.06.005
DO - 10.1016/j.trb.2015.06.005
M3 - 文章
AN - SCOPUS:84933039055
SN - 0191-2615
VL - 79
SP - 189
EP - 217
JO - Transportation Research Part B: Methodological
JF - Transportation Research Part B: Methodological
ER -