Continuous-space automaton model for pedestrian dynamics

An off-lattice automaton for modeling pedestrian dynamics is presented. Pedestrians are represented by disks with variable radius that evolve following predefined rules. The key feature of our approach is that although positions and velocities are continuous, forces do not need to be calculated. This has the advantage that it allows using a larger time step than in force-based models. The room evacuation problem and circular racetrack simulations quantitatively reproduce the available experimental data, both for the specific flow rate and for the fundamental diagram of pedestrian traffic with an outstanding performance. In this last case, the variation of two free parameters ($r_{\min }$ and $r_{\max }$) of the model accounts for the great variety of experimental fundamental diagrams reported in the literature. Moreover, this variety can be interpreted in terms of these model parameters.

Figure 1

Illustration of the contractile particle model. Particles on the left are not in contact. They have no zero desired velocities (${\mathbf{v}}_d$). Dashed circles represent the minimum and maximum radii. Particles on the right are in contact; therefore the escape velocities are present; also their radii are collapsed to the minimum.

Figure 2

Simulated circular racetrack utilized to measure the fundamental diagram of pedestrian traffic. The arrows indicate the direction and sense of the desired velocities (${\mathbf{e}}_{\mathrm{target}}^i$).

Figure 3

Experimental fundamental diagrams and the one obtained with the proposed model employing the “set of parameters 1”.

Figure 4

Experimental fundamental diagrams and the one obtained with the proposed model employing the “set of parameters 2”.

Figure 5

Details of one realization of the egress process with $L$ $=$ 1.2 m and “set of parameters 2”. (a) Snapshot of the process at $t$ $=$ 32 s. Each particle is represented by a dot; in the figure the size of the dot is fixed and similar to $r_{\min }$. (b) Two individual trajectories of two arbitrary particles.

Figure 6

Specific flow rate obtained from the simulation of the egress of a 20 m $\times$ 20 m room, with one exit. Number of people and exit width were varied accordingly (see text). Dashed lines indicate the experimental range. Errors lie between the symbol size.

Figure 7

Influence of varying the free model parameter $r_{\min }$ on the fundamental diagram.

Figure 8

Effect of varying the free model parameter $r_{\max }$ on the fundamental diagram.

Figure 9

Impact of varying the model parameter $\beta$ on the fundamental diagram.

Figure 10

Variation of the specific flow rate as a function of the escape speed ($v_e$).