## 3 DCMS Model
### DCMS Model Simulation Calculation Results and Discussion
#### 3.4.2 Total Comparison Times Results Statistics  
According to the evaluation system established in Section 3.2, the total comparison times of the roller groups for the unmixed group and mix groups 1-7 are calculated (two decimal places were retained). The statistical results for the total comparison times of each group are shown in Table 3.  
Based on the total comparison time data, the distribution of total comparison times for each group is computed. All total comparison times in the table are extracted and normalized, and the distribution of the number of roller groups in different total encounter time intervals is counted. Figure 9 depicts the distribution of total comparison times for each roller group under different leap probability \(k\) conditions. Figure 10 illustrates the distribution of total comparison times for each roller group under different leap space \(S_{n}\) conditions. The horizontal axis represents the total comparison times between the rollers after normalization, and the vertical axis represents the number of roller groups within that total comparison time interval. Figure 8: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Roller Number** & **0** & **1** & **2** & **3** & **4** & \(\ldots\) \\ \hline
0 & 7358.23 & 17,122.83 & 10,433.05 & 15,712.79 & 11,217.71 & \\ \hline
1 & 17,122.83 & 7913.05 & 14,967.20 & 19,572.99 & 15,597.04 & \\ \hline
2 & 10,433.05 & 14,967.20 & 7898.68 & 16,764.61 & 19,789.18 & \\ \hline
3 & 15,712.79 & 19,572.99 & 16,764.61 & 7993.97 & 17,140.94 & \\ \hline
4 & 11,217.71 & 15,597.04 & 19,789.18 & 17,140.94 & 7805.03 & \\ \hline
5 & 13,158.85 & 17,504.86 & 18,759.40 & 19,025.13 & 19,218.08 & \\ \hline
6 & 18,281.17 & 15,663.36 & 8221.31 & 13,823.81 & 8969.08 & \\ \hline
7 & 14,559.75 & 18,521.15 & 17,855.76 & 19,586.26 & 18,087.99 & \\ \hline
8 & 11,437.72 & 15,461.85 & 18,720.42 & 17,009.47 & 19,443.01 & \\ \hline
9 & 7689.97 & 9274.55 & 14,158.83 & 10,714.01 & 14,189.94 & \\ \hline
10 & 9815.62 & 13,666.55 & 18,979.74 & 15,646.42 & 19,089.09 & \\ \hline
11 & 7101.55 & 10,561.53 & 17,729.51 & 12,641.33 & 16,964.83 & \\ \hline
12 & 10,190.52 & 12,933.19 & 16,562.62 & 14,300.54 & 17,036.30 & \\ \hline
13 & 10,654.98 & 14,938.56 & 18,972.33 & 16,531.46 & 18,550.91 & \\ \hline
14 & 19,464.84 & 16,536.20 & 9255.95 & 14,814.04 & 10,048.13 & \\ \hline
15 & 16,989.42 & 18,944.55 & 14,775.37 & 18,930.10 & 15,191.15 & \\ \hline \end{tabular}
\end{table} 
Table 3: Partial results of total comparison times for unmixed group. Figure 8: Statistics of number of roller groups that did not participate in processing together under different leap space \(S_{n}\) conditions (leap probability \(k=0.3\)), (**a**) \(S_{n}=0\), (**b**) \(S_{n}=10\), (**c**) \(S_{n}=20\), (**d**) \(S_{n}=30\), (**e**) \(S_{n}=40\). Figure 9: Distribution of total comparison times of roller groups under different leap probability \(k\) conditions (leap space \(S_{n}=30\)), (**a**) \(k=0\), (**b**) \(k=0.1\), (**c**) \(k=0.2\), (**d**) \(k=0.3\), (**e**) \(k=0.4\). Figure 10: Distribution of total comparison times of roller groups under different leap space \(S_{n}\) conditions (leap probability \(k=0.3\)), (**a**) \(S_{n}=0\), (**b**) \(S_{n}=10\), (**c**) \(S_{n}=20\), (**d**) \(S_{n}=30\), (**e**) \(S_{n}=40\). Based on Figures 9a and 10a, we can identify two main issues with DDSGL that have not been implemented DCMS: (1) A large number of roller groups are distributed in intervals with fewer total comparison times, indicating insufficient size comparisons among some rollers in the entire batch; (2) There is a certain number of total comparison times in each interval from 0.2 to 1, suggesting significant differences in the total comparison times among different roller groups, leading to uneven size comparisons.