A modified social force model considering relative velocity of pedestrians

Social force model is a widely-used crowd model that simulates pedestrian dynamics based on Newtonian mechanics. It combines physical forces (caused by body compression) with psychological repulsive forces (caused by the pedestrians´ inner desire to keep a distance from others or walls) to represent the intentional collision avoidance mechanism. The model can reproduce many collective phenomena (e.g., lane formation, and the “faster is slower” effect). However, there are still things unrealistic in the original social force model. For example, we observe that when pedestrians approach a wall with different velocities, the repulsive forces exerted on them depend only on the distance between them and the wall. As a result, a pedestrian with a higher velocity may experience a stronger collision with the wall than others. However, in reality, he/she is able to predict this stronger collision, and would slow down much earlier than others. This paper introduces a modified social force model in which the pedestrians predict possible collisions using the information of not only positions, but also the velocities: pedestrians predict positions in the next time step based on the current positions and velocities, and the psychological repulsive forces on pedestrians are determined by the predicted positions instead of current positions. With this modified collision avoidance mechanism, pedestrians behave more realistic. Simulation results show that the modified model reduces the oscillation significantly and is more realistic. We also study the relationship between the total evacuation time and the time step of prediction in a specified scenario.