Study On The Characteristics Of Pedestrian Flow In Corridors Base On Continuum Dynamic Equilibrium Model

The study of pedestrian flow characteristics in urban rail transit is helpful to the rational allocation of rail transit space resources, making rail traffic facilities adapt to the dynamic traffic demand of pedestrian. So that it can improve the utilization rate of rail transit space and infrastructure capacity, and put forward the scientific and effective solutions to alleviate the rail transit congestion. At present, the model of traffic characteristics for pedestrian flow can be divided into macroscopic, mesoscopic and microscopic ones. Compared with the microscopic model, there are many advantages for the macroscopic model. First, it is particularly suited for depicting a large transportation system. Furthermore, it conveniently depicts a collective path-choice behavior of large amounts of travelers. Third, it has a good interpretation of dynamic and macroscopic variables of traffic system, such as traffic parameter changes of the velocity, density and flow rate. And it provides full information for the construction and management of urban rail transit.First, this paper analyses the characteristics of rail transit pedestrian flow and the macroscopic traffic characteristics, which laying theoretical basis for the establishment of the model And then builds the model at the second part, including deriving the continuity equation and improve the principles of pedestrian path choice. This paper uses the reactive dynamic user equilibrium principle to choice path, that the pedestrians choose a path which the cost is minimal according to the instantaneous traffic condition. And on the analysis of the existing research, this paper redefines the local travel function as a linear combination of travel time of walking unit distance and discomfort function. Moreover the relation of speed and density is fitted by the measured data. Finally constructs the continuum dynamic equilibrium model which is composed of conservation equation and Eikonal equation that depends on the traffic density implicitly. Actually, the conservation equation controls the spread of pedestrian speed, density and flow, and the Eikonal equation controls the direction of pedestrian flow. At the third part, this paper puts forward the numerical methods to solve the model. In the case of a known density, this paper adopts a Fast Sweeping Method based on third order WENO scheme to solve Eikonal equation. When solving the conservation equation, the five order WENO scheme is used to discrete flow on the space and the third order Lunge-Kutta is used to discrete density on time, so that we can obtain the density of the next moment. Finally, through the simulation of urban rail transit corridors which width changes direction or gradient like the funnel, the accuracy and scientific of the model and the algorithm are verified.