In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the travel cost to its destination in a reactive manner based on instantaneous information. The model consists of a conservation law equation coupled with an Eikonal-type equation for each group. The velocity-density relationship of pedestrian movement is obtained via an experimental method. The model is,solved using a finite volume method for the conservation law equation and a fast-marching method for the Eikonal-type equation on unstructured grids. The numerical results verify the rationality of the model and the validity of the numerical method. Based on this continuum model, a number of results, e.g., the formation of strips or moving clusters composed of pedestrians walking to the same destination, are also observed.

The analytical shock-fitting algorithm outperforms traditional numerical methods in solving the Lighthill-Whitham-Richards (LWR) traffic flow model for homogeneous highways. In this study, we extend the algorithm to an inhomogeneous highway in which two homogeneous sections with different fundamental diagrams are connected by a junction (interface). According to the entropy condition of the Riemann problem, the flow conditions at the interface can be categorized into four groups, and the density on both sides of the interface can be uniquely determined. Based on the physical conditions, we construct a fictitious element as an appropriate boundary condition for each homogeneous section. Consequently, the Riemann problem of an inhomogeneous highway can be transformed into a problem of equivalent homogeneous sections to which the shock-fitting algorithm can be applied. We apply this algorithm to some representative traffic flow cases and compare the results with numerical solutions obtained using the Weighted Essentially Non-Oscillatory (WENO) scheme. © Hong Kong Society for Transportation Studies Limited.

This paper extends the δ-mapping algorithm to solve a multi-class traffic flow model on an inhomogeneous highway, which is characterized by spatially varying fluxes and very complex waves. In the algorithm, the values of solution variables are mapped onto an intermediate state locally around the cell interface, and then the finite difference WENO reconstruction is applied. The hybrid scheme is consistent with steady flows, and resolves the waves more efficiently than the standard WENO scheme. The algorithm is also applicable to hyperbolic conservation laws with spatially varying fluxes in general. © 2008 Elsevier B.V. All rights reserved.

针对流通量间断双曲守恒方程的数值求解,构造了将δ-映射与经典的WENO（weighted essentially non-oscillatory）五阶有限体方法结合的混合算法,并用于求解具有混合介质的弹性波方程和流通量间断的多车种交通流模型方程.数值结果表明了算法的有效性.

This paper develops a higher-order macroscopic model of pedestrian crowd dynamics derived from fluid dynamics that consists of two-dimensional Euler equations with relaxation. The desired directional motion of pedestrians is determined by an Eikonal-type equation, which describes a problem that minimizes the instantaneous total walking cost from origin to destination. A linear stability analysis of the model demonstrates its ability to describe traffic instability in crowd flows. The algorithm to solve the macroscopic model is composed of a splitting technique introduced to treat the relaxation terms, a second-order positivity-preserving central-upwind scheme for hyperbolic conservation laws, and a fast-sweeping method for the Eikonal-type equation on unstructured meshes. To test the applicability of the model, we study a challenging pedestrian crowd flow problem of the presence of an obstruction in a two-dimensional continuous walking facility. The numerical results indicate the rationality of the model and the effectiveness of the computational algorithm in predicting the flux or density distribution and the macroscopic behavior of the pedestrian crowd flow. The simulation results are compared with those obtained by the two-dimensional Lighthill-Whitham-Richards pedestrian flow model with various model parameters, which further shows that the macroscopic model is able to correctly describe complex phenomena such as "stop-and-go waves" observed in empirical pedestrian flows. (C) 2010 Elsevier B.V. All rights reserved.

We propose a macroscopic model of lane-changing that is consistent with car-following behavior on a two-lane highway. Using linear stability theory, we find that lane-changing affects the stable region and the propagation speeds of the first-order and second-order waves. In analyzing a small disturbance, our model effectively reproduces certain non-equilibrium traffic-flow phenomena - small disturbance instability, stop-and-go waves, and local clusters that are affected by lane-changing. The model also gives the flow-density relationships in terms of the actual flow rate, the lane-changing rate, and the difference between the potential flow rate (the flow rate that would have occurred without lane-changing) and the actual flow rate. The relationships between the actual flow rate and traffic density and between the lane-changing rate and traffic density follow a reverse-lambda shape, which is largely consistent with observed traffic phenomena.

In a recent paper, the weighted essentially non-oscillatory (WENO) numerical scheme was applied to solve a multi-class Lighthill-Whitham-Richards (MCLWR) traffic flow model (J. Comput. Phys. 2003; 191:639-659). We discuss and present an enhanced WENO scheme with Lax-Friedrichs flux splitting by improving the estimation of the minimal characteristic speed of the MCLWR model, which is based on a set of inequalities of eigenvalues. Copyright (C) 2009 John Wiley & Sons, Ltd.

This paper takes into account three regimes for the description of traffic dynamics, which include the introduction of a pseudo-density transformed from the velocity, the pressure as a function of the pseudo-density and the relaxation of velocity to equilibrium. The resultant characteristic variables can be used to measure the deviation of the phase state to a desired state and derive physically bounded solutions. Taking the pseudo-density as a conserved variable, the approach is able to describe both equilibrium and non-equilibrium flows in a systematic and unified manner, and thus complex traffic phenomena. The theoretical properties of the model are thoroughly investigated, and numerical examples are used to demonstrate the ability of the model to reproduce some notable traffic phenomena. © 2008 Elsevier Ltd. All rights reserved.

A mutinomial logit model of urban taxi services has been developed for the study of the operational characteristics of the taxi industry, in which it is hypothesised that the customer-searching behaviour of vacant taxis follows a multinomial logit choice model. Although the model is commonly used, little empirical evidence exists to validate the choice mechanism and determine the set of important factors that affect the choice. In the present study, a stated preference survey of 400 taxi drivers was conducted to analyse the customer-searching behaviour of vacant taxis. The results explain how the considered parameters of waiting time, journey time, travel distance and toll affect the driver behaviour when searching for customers. In addition, market segmentation analysis was carried out to study the effects of driver demographics and operational characteristics on the searching behaviour. The parameters that were considered in this section of the study were the age of the driver, taxi ownership, driver experience and marital status.

In this paper, we develop a model of bidirectional pedestrian streams with an oblique intersecting angle that represents the crossing interaction of pedestrians moving in different directions on a walking facility. We formulate the model based on Drake's model in the traffic flow literature, and calibrate it using results from a set of controlled experiments in which two groups of pedestrians were asked to walk in different directions and cross on designated walkways with different levels of pedestrian flow and different intersecting angles. Their movements were video recorded, and macroscopic quantities such as speed, density, and flow were extracted to calibrate the model of bidirectional pedestrian streams. All of the parameters of the calibrated model are statistically significant at the 0.1% level.