# A Study on Crowd Evacuation Model Considering Squeezing Equilibrium in Crowded Areas
## 1 Introduction
[29] introduced the concepts of pedestrian congestion, support and friction by referring to the social force model, designed an extended cellular automata model to study the behavior of pedestrian stampede events, discussed the stampede phenomenon during the pedestrian evacuation in public places, and explored the impact of pedestrian density, pedestrian distribution mode, exit setting and exit obstacles on the evacuation results. By studying the evacuation dynamics of pedestrians in a square room with a single exit, [PERSON] et al. [30; 31] found that personal interests may have a positive or negative impact on evacuation dynamics, depending on whether it can promote the formation of collective cooperation, and discussed the impact of setting obstacles in front of the exit and the diversity of pedestrians' responses to space competition on evacuation dynamics. [PERSON] et al. [32] successfully reproduced the evacuation drills using the modified social force model and developed a new library to simulate the dynamics of pedestrian flow. As the lack of competitive behavior may inhibit the effect of \"faster is slower\", competitive behavior was a key factor of the \"faster is slower\" effect. [PERSON] et al. [33] studied the function of spatial constraint layout and the impact of movement speed level on the evacuation performance of pedestrian facilities, especially for dense crowds. Under certain geometric constraints, it was more likely to form congestion (i.e., a longer queue or a longer time interval between two consecutive pedestrians pass). The examination of trajectory model shows that this may be attributed to the extent to which two flows must mix with each other in order to merge and share space. Some layouts, especially symmetric layouts, allowed the two flows to remain separate once they entered the shared space, while other settings produced a more pronounced mixture of motion trajectories so that the two flows could cross the shared area. [PERSON] et al. [34] established a density navigation field model based on equipotential field and proposed a density navigation algorithm. They also calculated the density factor and distance factor to guide the target selection during crowd movement and combined the density evacuation algorithm and social force model to simulate crowd evacuation, and thus effectively improve the evacuation efficiency us ing a two-tier mechanism. [PERSON] et al. [35] used a finite volume-finite element hybrid method to solve the problem, and performed error analysis on the solver, gradient calculation, and second-order model to obtain the first-order convergence and prove that [PERSON] model could not reproduce complex crowd dynamics such as stop-and-go waves and congestion at the bottleneck. [PERSON] et al. [36] developed a multi-grid cellular automaton model to study the impact of sideways movement and opening the evacuation process, indicating that turning behavior shortened the escape time and moderate turning speed was the best choice for evacuation. [PERSON] et al. [37] combined the exit choice model and the social force model with pedestrian classification and explored the effects of distance and density weight coefficient in the exit choice model on evacuation time. The results show that with an increase in the density weight coefficient of the luggage-laden pedestrian, the evacuation time initially decreases and then increases. The evacuation time was shortened as the pedestrian density's standard deviation at exits decreased, and the evacuation time was extended otherwise. In addition, the number of luggage-laden pedestrians is the main factor that leads to an increase in evacuation time. Considering the distance between pedestrians and exits, the pedestrian density near the exit and the exit width, [PERSON] et al. [38] constructed a pedestrian multi-exit selection model based on the social force model and simulated and analyzed the impact of pedestrian density near the exit and the exit width. [PERSON] et al.