# A Study on Crowd Evacuation Model Considering Squeezing Equilibrium in Crowded Areas
## 1 Introduction  
In recent years, stampede accidents have occurred frequently, resulting in heavy casualties and property losses. The research on pedestrian and evacuation dynamics has attracted the attention of scholars at home and abroad, and the study of crowd evacuation is of great significance to guaranteeing the controllability of stampede accidents and reducing accident casualties [1]. During the evacuation, the motion dynamics of human beings in a crowded building environment is affected by the interaction between individuals and their physical environment, especially when the geometric space of movement is restricted. In a complex and dense scene, the acting force between pedestrians and between pedestrians and obstacles has an important impact on evacuation time and efficiency. Therefore, exploring the relationship between evacuation time and acting force (degree of squeezing) is particularly important for effective crowd evacuation. At present, the model used to study the crowd behavior characteristics is mainly divided into macromodel and micromodel. The earliest macroscopic model was proposed by [PERSON] [2], who used the Maxwell-Boltzmann distribution of thermodynamics to give the probability distribution formula of the human forward speed, and the relationship between the forward speed and various factors is studied by using the formula. Macromodels mainly include fluid dynamics models [3] and so on. [PERSON] et al. [4] transformed the mesoscopic concept from traffic flow to pedestrian flow, proposing a mesoscopic evacuation model that uses nodes and links to express macroscopic concepts thatfocus on the movement of crowds rather than on the movement of individuals. [PERSON] et al. [5] proposed a mesoscopic evacuation model and developed a new set of static field algorithms for mesoscopic evacuation modeling. The macromodel considers a large number of people as a whole and cannot take into account the individual's different psychological responses, personality characteristics, individual behavior and other factors [6]. Micromodel is a simulation model based on individual behavior characteristics, which can effectively describe the interaction between individuals, mainly including continuous and discrete models. The social force model is a typical representative of continuous models [7; 8; 9; 10; 11; 12; 13], while cellular automata model and lattice gas model are typical representatives of discrete models [14; 15; 16; 17; 18; 19; 20; 21; 22]. [PERSON] et al. [23] made use of the social force model early to study the formation mechanism of phenomena such as \"faster is slower\" and \"arching\" in the process of pedestrian evacuation, as well as the changes in behavior characteristics of the crowd. [PERSON] et al. [24] proposed an extended social force queueing model which is based on vision and morality. This model successfully predicts the emergence of the \"detours\" phenomenon, which is beneficial for reducing crowd pressure. [PERSON] et al. [25] improved the cellular automata model based on the difference in the crowd in the choice of direction viewability and the blurred viewability in walking direction and the pedestrian density at exits, so as to avoid the impact on the weight of factors related to transition probability. With a view of improving the cellular automata evacuation model, [PERSON] et al. [26; 27] made use of the effect of crowding force, resultant force parameter, absorption coefficient and anti-casualty coefficient to describe the effect of crowding force on individual pedestrians, as well as the absorption and resistance effect during the transmission of crowding force. Considering that pedestrians were unfamiliar with the evacuation environment, that is, pedestrians could not specify the location of the exit, [PERSON] et al. [28] compared the path choices and evacuation strategies of pedestrians with complete and incomplete evacuation information by dividing the evacuation space into different areas and employing the improved \"social force model\". [PERSON] et al.