Collective dynamics of pedestrians in a non-panic evacuation scenario

We present a study of pedestrian motion along a corridor in a non-panic regime (e.g., schools, hospitals or airports). Such situations have been discussed so far within the Social Force Model (SFM). We suggest to enrich this model by interactions based on the velocity of the particles and some randomness, both of which we introduce using the ideas of the Vicsek Model (VM). This new model allows to introduce fluctuations for a given average speed and geometry, and considering that the alignment interactions are modulated by an external control parameter (the noise $\eta$) allows to introduce phase transitions between ordered and disordered states. We have compared simulations of pedestrian motion along a corridor using (a) the VM with two boundary conditions (periodic and bouncing back) and with or without desired direction of motion, (b) the SFM, and (c) the new model SFM+VM. The study of steady-state configurations in the VM with confined geometry shows the expected bands perpendicular to the motion direction, while in the SFM and SFM+VM particles order in stripes of a given width $w$ along the direction of motion. The results in the SFM+VM case show that $w(t)\simeq t^\alpha$ has a diffusive-like behavior at low noise $\eta$ (dynamic exponent $\alpha \approx 1/2$), while it is sub-diffusive at high values of external noise ($\alpha \approx 1/4$). We observe the order-disorder transition in the VM with both boundary conditions, but the application of a desired direction condition inhibits the existence of disorder as expected. For the SFM+VM case we find a susceptibility maximum which increases with system size as a function of noise strength indicative of a order-disorder transition in the whole range of densities and speeds studied. From our results we conclude that the new SFM+VM model is a well-suited model to describe non-panic evacuation with diverse degrees of disorder.