Research Article: A microscopic simulation model for pedestrian-pedestrian and pedestrian-vehicle interactions at crosswalks

Date Published: July 17, 2017

Publisher: Public Library of Science

Author(s): Manxia Liu, Weiliang Zeng, Peng Chen, Xuyi Wu, Charlotte K. Hemelrijk.


This study aims to develop a microscopic pedestrian behavior model considering various interactions on pedestrian dynamics at crosswalks. Particularly, we take into account the evasion behavior with counter-flow pedestrians, the following behavior with leader pedestrians, and the collision avoidance behavior with vehicles. Aerial video data at one intersection in Beijing, China are extracted for model calibration. A microscopic calibration approach based on maximum likelihood estimation is applied to estimate the parameters of a modified social force model. Finally, we validate step-wise speed, step-wise acceleration, step-wise direction change, crossing time and lane formation phenomenon by comparing the real data and simulation outputs.

Partial Text

Studying the self-organization phenomena of pedestrian crowd is an active subject in transportation science. To date, pedestrian behavior modeling has attracted considerable attentions [1–7]. A better understanding of the interaction behavior would help to improve microscopic simulation and thus allow more accurate prediction of their behavior for various situations. This also helps to evaluate the service and safety level on pedestrian related traffic, such as pedestrian movement in urban streets and crosswalks.

As shown in Fig 1, the microscopic model includes two layers, i.e., a tactical layer and an operational layer, inspired by Hoogendoorn and Bovy’s conceptual modeling framework [48]. The desired direction of movement is determined in the tactical layer. The operational layer determines the microscopic behavior when pedestrians interact with other agents. In this layer, we assume that the subject pedestrian interacts with other pedestrians and vehicles. The interaction with surrounding pedestrians can be further divided into two types, i.e., interaction with counter-flow pedestrians and interaction with leading pedestrians. A repulsive force is used to represent the interaction with counter-flow pedestrians, while an attractive force is used to represent the interaction with leading pedestrians. The pedestrian-vehicle conflict mechanism is also included in this model. Risk-taking pedestrians might enter the crosswalk even though the vehicle is approaching. We model the “waiting/crossing” behavior with a bi-logit model and develop detour route plan and repulsive force model for pedestrian-vehicle interaction. The detail of the pedestrian behavior in the tactical and the operational layers is introduced in the following sections.

As shown in Fig 10, the empirical data were extracted using aerial videos captured by an optical camera with a 1920 × 1080 resolution mounted on a quadrotor with the flight altitude of about 40m-60m above the ground. The trajectories of pedestrians and turning vehicles at one intersection in Beijing, China were extracted from the video every 0.04s for model calibration. The dataset consists of the trajectories of 904 pedestrians and 156 turning vehicles. In total, 55,300 position samples are available. The available observations are trajectory profiles based on time series. From these data, all relevant quantities can be derived either directly or by applying finite differences, such as positions, velocities, accelerations, distances between pedestrians, and direction change.

Table 1 shows the parameter estimation for the distribution of exit position in Eqs (4) and (5). A parameter has statistical significance at a 95% confidence level if the p-value is less than 0.05. All of the parameters are statistically significant, indicating that the explanatory variables are meaningful. A positive sign of parameters means that the dependent variable increases as the explanatory variable value increases, while a negative sign means that the dependent variable decreases as the explanatory variable value increases. Interestingly, it is found that the increase in crosswalk length, crosswalk width and pedestrian density will lead to the increase of variation of exit position.

A two-layer microscopic model is presented to simulate the interactions between pedestrians and vehicles at signalized intersections. A modified social force model considering the evasion behavior with counter-flow pedestrians, the following behavior with the leader pedestrians, and the collision avoidance behavior with vehicles was developed. The calibration is undertaken using the trajectory data (samples are given in S1 Table) of pedestrians and vehicles at one intersection in Beijing, China. The parameters of the developed model are calibrated by a two-dimensional MLE. Finally, the model performance is verified by comparing observed and estimated pedestrian flow characteristics, such as speed, acceleration, direction change, fundamental diagram and lane formation.




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