Revisiting Jiang’s dynamic continuum model for urban cities

Abstract

Jiang et al. (Transportation Research Part B, 2011, 45(2), 343-363) proposed a predictive continuum dynamic user-optimal (PDUO-C) model to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers. Their modeled region is a dense urban city that is arbitrary in shape and has a single central business district (CBD). However, we argue that the model is not well posed due to an inconsistency in the route-choice strategy under certain conditions. To overcome this inconsistency, we revisit the PDUO-C problem, and construct an improved path-choice strategy. The improved model consists of a conservation law to govern the density, in which the flow direction is determined by the improved path-choice strategy, and a Hamilton-Jacobi equation to compute the total travel cost. The simultaneous satisfaction of both equations can be treated as a fixed-point problem. A self-adaptive method of successive averages (MSA) is proposed to solve this fixed-point problem. This method can automatically determine the optimal MSA step size using the least squares approach. Numerical examples are used to demonstrate the effectiveness of the model and the solution algorithm.

Reformulating the Hoogendoorn–Bovy predictive dynamic user-optimal model in continuum space with anisotropic condition

“…Note that by taking a special condition that hðñÞ ¼ 1, our anisotropic model will reduce back to Du et al (2013) model where the free-flow speed is isotropic. In this case, the speed intensity and the local travel cost are independent of the travel directionñ:…”

Numerical Simulation of Pedestrian Flow Based on A Higher-Order Macroscopic Model

“…For equilibrium traffic flow, there are two traffic assignment patterns, namely user equilibrium (UE) and system optimum (SO) [6][7][8]. The UE models encompass predictive UE models [9], in which pedestrians have predictive information when they are making a path-choice decision, and reactive dynamic user equilibrium models [7,10], in which pedestrians have to rely on the instantaneous information available to them and make their choices.…”

“…It is presumed that pedestrians have predictive information about traffic conditions over time and the desired direction of pedestrian movement is always to minimize the actual travel cost from the current position and time to the destination, thus resulting in a predictive UE pattern for the dynamic system [6,9].…”

“…(4) and (7) , the fast sweeping method to solve Eq. (8), and the self-adaptive MSA [9] to solve the discrete fixed-point problem.…”

“…Therefore, the discrete model is a fixed-point problem that can be solved by the MSA. See [9] for the description of MSA in detail.…”