Model framework.

<p>The microscopic model includes two layers, i.e., a tactical layer and an operational layer. The desired direction of movement is determined in the tactical layer. The operational layer determines the microscopic behavior when pedestrians interact with other agents.</p

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

<div><p>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.</p></div

Desired exit position and desired direction.

<p>The desired direction is assumed to be determined by the desired exit position of the crosswalk. The desired exit position is defined as the intersecting point of the curve of crosswalk edge and the desired walking trajectory.</p

Pedestrian-vehicle conflict.

<p>There are two types of pedestrian giving-way maneuvers when the pedestrian-vehicle conflict occurs: waiting until the vehicle passes by and crossing before the vehicle passes by.</p

Simulation performance on speed, acceleration, direction change and crossing time.

<p>(a) shows the average absolute error of walking speed. (b) shows the comparison of step-wise acceleration distributions. (c) shows the distribution of the step-wise direction change between current and previous directions. (d) shows the distribution of the crossing time at crosswalk.</p

Trajectory comparison.

<p>(a) shows the pedestrian trajectories from real data and (b) shows simulation outputs.</p

Fundamental diagrams of pedestrian flow.

<p>The simulated fundamental diagrams are in good agreement with the observed ones.</p

Collision avoidance with counter-flow pedestrians.

<p>(a) It is usually assumed that the magnitude of the repulsive force increases monotonically as the relative distance decreases. (b) It shows the case of valid and invalid conflicts.</p

Lower layer: Repulsive force.

<p>A vehicle is now represented by an ellipse with the radius which depends on the angle between the moving direction of the vehicle and the moving direction of a close-by pedestrian.</p