# A Study on Crowd Evacuation Model Considering Squeezing Equilibrium in Crowded Areas
## 4 Simulation Experiment  
### Data Processing Method  
The simulation experiment is conducted based on the relational expression of parameters \(h1\), \(h2\) and \(h3\) above. Many experiments have shown that the best values of \(h1\), \(h2\) and \(h3\) are 12,000, 24,000 and 120,000, respectively, and satisfy the Formula (25) so that pedestrians are less likely to evacuate disorderly in dense areas. The original model and the optimized model are compared by actual simulation experiments and data processing methods. Among them, the extent of contact between pedestrians or between pedestrians and obstacles is similar, so the simulation data processing method is only available to discuss the extent of contact between pedestrians, and the extent of contact is regarded as three independent variables:  
\(x1\): intersection and less than the maximum degree of squeezing d \(>\) 0 and \(d<\) f; \(x2\): intersection exceeding the maximum degree of squeezing, \(d\geq\) f; \(x3\): separation \(d<\) 0; \(d\) is the extent of contact, as follows:  
\[d=2r-\sqrt{p_{i}{(x,y)}^{2}-p_{j}{(x,y)}^{2}} \tag{26}\]  
In dense scenes, the probability of pedestrians under the three extents of contact above is calculated and expressed as follows:  
\[f(xi)=\left\{ \begin{array}{l}f(x1)+1,\ d>0,d<r/8\\ f(x2)+1,\ d>r/8\\ f(x3)+1,\ d<0\end{array} \right. \tag{27}\]  
where, _i,j_ is the id of a pedestrian, \(d\) is the degree of contact between pedestrians, \(p(x\),\(y)\) is the coordinate of a pedestrian, \(r\) is the radius of a pedestrian, and \(f(xi)\) is the number of times that a pedestrian satisfies an extent of contact at a certain time. \[p(xi)=\frac{f(xi)}{n} \tag{28}\]  
where, \(n\) is the total number of evacuated pedestrians, and \(p(xi)\) is the probability of satisfying an extent of contact and satisfies \(\sum_{i}^{3}p(xi)=1\). The probability of satisfying an extent of contact calculated by the original social force model is \(p_{1}(xi)\), the probability of satisfying an extent of contact calculated by the optimized social force model is \(p_{2}(xi)\), \(xi\in(x1,x2,x3)\). Obviously, the results are correct if the following phenomena occur. \[p_{1}(x1)>p_{2}(x1),p_{1}(x2)>p_{2}(x2) \tag{29}\]  
Figure 4: Evacuation simulation of optimized model in the scene 2: (**a**) T = 0 s; (**b**) T = 10 s; (**c**) T = 20 s.  
Figure 5: Evacuation simulation of original model in the scene 3: (**a**) T = 0 s; (**b**) T = 10 s; (**c**) T = 20 s.  
Figure 3: Evacuation simulation of original model in the scene 2: (**a**) T = 0 s; (**b**) T = 10 s; (**c**) T = 20 s.  
Figure 8: Evacuation simulation of optimized model in the scene 4: (**a**) T = 0 s; (**b**) T = 10 s; (**c**) T = 20 s.  
Figure 6: Evacuation simulation of optimized model in the scene 3: (**a**) T = 0 s; (**b**) T = 10 s; (**c**) T = 20 s.  
Figure 9 shows the data of the degree of squeezing of the original model and the optimized model in three different cases in the scene 1. When T = 1 s to T = 10 s, the probability \(p(x1)\) of the original model increased dramatically and the optimized model was relatively stable; the probability \(p(x3)\) of the original model decreased dramatically and the optimized model was relatively stable; the probability \(p(x2)\) of the original model was roughly the same as that of the optimized model. This suggests that the original model and the optimized model have the same ability to control the probability of exceeding the maximum squeezing range, but the optimized model shows better stability in the ability to control the intersection without exceeding the maximum degree of squeezing. Further, the comparison of three different scenarios (Figures 10-12) shows that because of the simplicity of scenario 2 and scenario 3, the original model and the optimized model have the same ability to control the intersection and not more than the maximum extrusion degree, and the optimized model is obviously better than the original model.