Social Force Model for Pedestrian Dynamics

TL;DR

The paper addresses quantitative pedestrian dynamics by proposing a social force framework in which each pedestrian's motion is steered by a relaxation toward a desired velocity and by force-like interactions with others and borders. It formalizes $d w_α/dt = F_α(t) + fluctuations$ and $v_α(t) = w_α(t) g(v_α^{max}/||w_α||)$, with $F_α(t)$ combining $F_α^{0}$, repulsive and attractive interactions, and directional perception weights. The model yields nonlinear Langevin equations whose simulations reproduce self-organized lane formation and oscillatory flows at bottlenecks, validating the approach against observed crowd behaviors. The work provides a tractable, data-consistent framework for planning pedestrian spaces and suggests extensions to route-choice and other social phenomena.

Abstract

It is suggested that the motion of pedestrians can be described as if they would be subject to `social forces'. These `forces' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal motivations of the individuals to perform certain actions (movements). The corresponding force concept is discussed in more detail and can be also applied to the description of other behaviors. In the presented model of pedestrian behavior several force terms are essential: First, a term describing the acceleration towards the desired velocity of motion. Second, terms reflecting that a pedestrian keeps a certain distance to other pedestrians and borders. Third, a term modeling attractive effects. The resulting equations of motion are nonlinearly coupled Langevin equations. Computer simulations of crowds of interacting pedestrians show that the social force model is capable of describing the self-organization of several observed collective effects of pedestrian behavior very realistically.

Figures (5)

• Figure 1: Schematic representation of processes leading to behavioral changes.
• Figure 2: Above a critical pedestrian density one can observe the formation of lanes consisting of pedestrians with a uniform walking direction. Here, the computational result shows $N = 4$ lanes on a walkway that is 10m wide and 50m long. Empty circles represent pedestrians with a desired direction of motion which is opposite to that of pedestrians symbolized by full circles.
• Figure 3: The average number $N$ of lanes emerging on a walkway scales linearly with its width $W$ ($N(W) = 0.36\hbox{m}^{-1} W + 0.59$).
• Figure 4: If one pedestrian has been able to pass a narrow door, other pedestrians with the same desired walking direction can follow easily whereas pedestrians with an opposite desired direction of motion have to wait. The diameters of the circles are a measure for the actual velocity of motion.
• Figure 5: After some time the pedestrian stream is stopped, and the door is captured by individuals who pass the door into the opposite direction.