Experimental study of the behavioural mechanisms underlying self-organization in human crowds

Abstract

In animal societies as well as in human crowds, many observed collective behaviours result from self-organized processes based on local interactions among individuals. However, models of crowd dynamics are still lacking a systematic individual-level experimental verification, and the local mechanisms underlying the formation of collective patterns are not yet known in detail. We have conducted a set of well-controlled experiments with pedestrians performing simple avoidance tasks in order to determine the laws ruling their behaviour during interactions. The analysis of the large trajectory dataset was used to compute a behavioural map that describes the average change of the direction and speed of a pedestrian for various interaction distances and angles. The experimental results reveal features of the decision process when pedestrians choose the side on which they evade, and show a side preference that is amplified by mutual interactions. The predictions of a binary interaction model based on the above findings were then compared with bidirectional flows of people recorded in a crowded street. Simulations generate two asymmetric lanes with opposite directions of motion, in quantitative agreement with our empirical observations. The knowledge of pedestrian behavioural laws is an important step ahead in the understanding of the underlying dynamics of crowd behaviour and allows for reliable predictions of collective pedestrian movements under natural conditions.

Figure 1

(a) Snapshot of the experimental set-up. Red circles indicate the location of cameras. (b) Calibration of the acceleration behaviour on the basis of the average time-dependent pedestrian velocity in the absence of interactions. The fitted curve (blue, simulation) is given by the acceleration equation (4.1). The parameters were estimated as τ=0.54±0.05 s and v₀=1.29±0.19 m s⁻¹ after a reaction time of 0.35 s (red solid and dashed lines, data+s.d.).

Figure 2

Observed trajectories in (a) condition 2 (N=148) and (b) condition 3 (N=123). One of the pedestrians (moving from left to right) is represented in blue, while the other one is represented in red.

Figure 3

(a) Average value of the interaction effect f_ij at various distance d_ij and angle θ_ij during experimental condition 2. (b) For a given angle θ, the function f_θ(d, θ) describing the directional changes, (i) θ=4°; (ii) θ=9°; (iii) θ=17°, decreases exponentially with d, which provides the relation , with fit parameter b. (c) A(θ) can then be approximated by the equation , where K is the sign of θ and a, c are fit parameters. The function f_v(d, θ) for speed changes has been set according to a similar functional dependency.

Figure 4

Numerical simulations as compared to experimental observations during conditions 2 and 3. In (a,b), the blue lines correspond to the average observed trajectories, with pedestrians moving from left to right. The blue dashed lines indicate the standard deviation. Red lines correspond to the average trajectories obtained after 1000 simulations (with parameter values A=4.5, n=2, n′=3 and 0.005). Bars in (c,d) indicate the proportions of choosing the left- or right-hand side in an avoidance manoeuvre during the experiment (blue bars) or in simulations (red bars).

Figure 5

Asymmetry of bidirectional pedestrian traffic. As sketched in (a) six areas of the street were distinguished for the measurements: (1) left sidewalk, (2) and (3) left side of the walkway, (iv) and (5) right side of the walkway, and (6) right sidewalk. ‘Left’ and ‘right’ are referring to the walking direction. The sidewalks next to shops were occupied by a small number of standing pedestrians. The blue bars in (b) show the proportion of observed pedestrians walking in each area, while the red bars are simulation results (with the same parameter values as in figure 4). For comparison, the inset illustrates the symmetric simulation results for a unidirectional flow.