## 3 DCMS Model
### DCMS Evaluation System  
In the established DCMS model, the movement of the entire batch of rollers within the DDSGL system in actual processing scenarios can be simulated. It is necessary to extract related data during the operation of the model, establish a DCMS evaluation system, and explore whether DCMS can enable the entire batch of rollers to fully compare sizes in the processing area. In the DCMS model, the positions and numbers of all rollers in the processing area at each processing step can be recorded. The number of times \(C_{d}\) that two rollers with different numbers directly participate in processing in the processing area can be counted. The data counting method is shown in Figure 6. A \(n\times n\) table is established based on the processing batch of rollers as \(n\). Both the title row and title column are roller numbers, and each position in the table matrix is used to record the number of direct comparisons when rollers with the row and column title numbers participate in processing together. In each processing step, each pair of rollers in all processing spaces A are directly compared once, and the number at the position corresponding to the two roller numbers in the statistics table is increased by 1. For example, in processing step 1 in Figure 6, rollers numbered 1-8 all participate in comparison processing once, so the number in the yellow area of the statistics table for processing step 1 is increased by 1. In processing step 2, according to the roller operation rule shown in Figure 5, roller number 1 moves out of the processing area, and roller number 9 moves into the processing area, so the data record in the new yellow area in the statistics table is increased by 1, and so on. It should be noted that, before the inclusion of DCMS, the rollers entered the processing area in sequence according to the order of the numbers in the model. After DCMS is included, the order of roller numbers will be disrupted, as shown in processing step 3 in Figure 6. When roller number 11 enters the processing area, the yellow area where data is updated in the statistics table will also be split according to the roller number. In the DDSGL experiments without the inclusion of the DCMS, a large number of rollers did not undergo direct size comparison in the processing region. Nevertheless, the batch diameter change of the rollers was still convergent, indicating that two rollers that have not directly participated in processing can achieve indirect size comparison through other rollers, thereby achieving the effect of size convergence for the entire batch of rollers. Therefore, the introduction of the indirect comparison factor, based on direct comparison, will be closer to the actual processing process. Direct and indirect comparisons between rollers are akin to close and secondary contacts in epidemiological research. For example, Roller 1 and Roller 2 directly compare sizes as they both participate in processing, and Roller 2 and Roller 3 ensure the same. In this case, Roller 1 and Roller 3 are defined as being indirectly compared, with Roller 2 serving as the mediator for this indirect comparison between Rollers 1 and 3. It should be noted that this chapter only accounts for one level of indirect comparison (secondary close contact level), and multiple levels of indirect comparison are not considered. To facilitate data collection, appropriate calculation rules need to be established between direct and indirect comparisons. For example, an indirect comparison between Roller 1 and Roller 3 mediated by Roller 2 could be equivalent to a certain number of direct comparisons between Roller 1 and Roller 3. According to the processing principle of DDSGL, the final diameter size of Roller 2 is the result of its initial diameter size and the diameter sizes of other rollers. One could calculate the proportion of the number of direct comparisons between Roller 1 and Roller 2 (\(C_{12}\)) to the total number of direct comparisons between Roller 2 and all rollers (\(C_{2}\)).