A predictive continuum dynamic user-optimal model for a polycentric urban city

Abstract

A*predictive*continuum*dynamic*useroptimal*model*for*a*polycentric*urban*city

Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

“…Notice that the initial time in the CL portion is t = 0, whereas in the HJ portion the initial time is t = t end . Lin et al [39] extend the model proposed by Du et al [10] to a polycentric urban city, where the speed and local cost per unit distance are computed separately for each group of vehicles based on (22) and (23), respectively, using the total density instead of the individual density of each group. Hoogendoorn and Bovy [17] develop a pedestrian PDUE model for multiple pedestrian groups, where each group has a different destination, as…”

A Continuum Model for Cities Based on the Macroscopic Fundamental Diagram: a Semi-Lagrangian Solution Method

“…This equation is well understood in the context of steady incompressible, irrotational fluid flow on the plane. Finally, to incorporate multiple destinations and/or multiple types of users, multi-commodity extensions of Hughes' model have been proposed exclusively in Eulerian coordinates for the multi-CBD city networks (Lin et al, 2017) and for the bi-directional pedestrian flow (see e.g., Huang et al, 2009b, Jiang et al, 2009, 2012. Separate potential functions are defined for each destination and the optimum movement direction of the travelers moving toward each of the destinations is found by the corresponding potential function.…”

“…Continuum-space models started earlier with the seminal work by Hughes (2002), and are typically formulated as a system of two partial differential equations (PDE), a two-dimensional (2-D) conservation law for the density, ρ, coupled with a PDE for the route choice, typically of the Eikonal or Hamilton-Jacobi type, either for vehicular traffic (see e.g., Jiang et al, 2011, Du et al, 2013, Lin et al, 2017 or for pedestrian flow (see e.g., Huang et al, 2009a,b, Jiang et al, 2009, 2010, 2012, Hoogendoorn and Bovy, 2004, Hoogendoorn et al, 2015.…”

A decision support and planning mobility method for large scale traffic networks

“…However, all these models allow only the representation of a unique direction of flow. These models have a unique flow direction and to the best of our knowledge the only extension to multiple direction is [19]. One way to accomodate the multiple directions of flow is to extend the existing model in [18] to a system of conservation laws.…”