# Fast and Effective Tag Searching for Multi-Group RFID Systems
## 7 Performance Evaluation
### Simulation Results  
In Figure 5, we set the target tags ratio \(\lambda=0.3\) and the reliability requirement \(P_{req}=0.999\). Then, we explore its impact on the time efficiency of our protocols by changing the number of local tags in each group from 1000 to 5000 by 1000 in Figure 5a,c and from 500 to 2500 by 500 in Figure 5b. It should be noted that the number of local tags in each group here refers to the average number. Taking Figure 5a as an example, we set the number of groups \(G=21\), the group interval \(r=10\), and the number of wanted tags in each group \(|W_{g}|=1000\). It means that there are 21 groups in the local tag set, and the number of local tags in these groups is changing from 900 to 1100 by 10. We set the number of groups \(G=41\), the group interval \(r=10\) and the number of wanted tags in each group \(|W_{g}|=500\) in Figure 5b, and set the number of groups \(G=21\), the group interval \(r=20\), and the number of wanted tags in each group \(|W_{g}|=1000\) in Figure 5c. As you can see, the number of local tags for each group in Figure 5b is different from the other two figures because the group number in Figure 5b is different from the other two, and we must ensure the total number of local tags is consistent overall. This also applies to the number setting of wanted tags. We find that A-Search performs the best, followed by G-Search, and B-Search ranks third. In Figure 5a, when the number of local tags in each group \(|L_{g}|=2000\), the time cost of B-Search, G-Search, and A-Search equals 9.63 s, 9.43 s, and 9.39 s. The time cost of A-Search is 97.47% of B-Search and 99.57% of G-Search. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(G=21,W_{g}=1000\) & \(G=21,W_{g}=5000\) & \(G=41,W_{g}=1000\) & \(G=41,W_{g}=5000\) \\ \hline Baseline & 34.95 & 174.73 & 68.24 & 341.14 \\ \hline B-Search & 10.86 & 53.17 & 21.23 & 103.81 \\ \hline G-Search & 10.71 & 53.00 & 20.90 & 103.46 \\In Figure 6, we set the target tag ratio \(\lambda=0.3\) and the reliability requirement \(P_{req}=0.999\). Then, we set the number of group \(G=21\), the group interval \(r=10\), and the number of local tags in each group \(|L_{g}|=5000\) in Figure 5(a). Set the number of groups \(G=41\), the group interval \(r=10\), and the number of local tags in each group \(|L_{g}|=2500\) in Figure 5(b). Set the number of groups \(G=21\), the group interval \(r=20\), and the number of local tags in each group \(|L_{g}|=5000\) in Figure 5(c). We explore its impact on the time efficiency of our protocols by changing the number of wanted tags from 1000 to 5000 by 1000 in Figure 5(a),c and from 500 to 2500 by 500 in Figure 5(b). Clearly, A-Search outperforms the other protocols. In Figure 5(a), when the number of wanted tags \(|W_{g}|=2000\), the time cost of B-Search and G-Search are 19.40 s and 19.72 s. The time cost of A-Search is 19.14 s, which is 98.65% of B-Search and 97.06% of G-Search. In this case, G-Search does not perform as well as B-Search. Because our method is not well suited for the situations where wanted tags are too many, and the fact that G-Search applies the longest frame length to all groups, inadvertently magnifying this disadvantage even more. In Figure 7, we set the number of local tags in each group \(|L_{g}|=2000\), the number of wanted tags in each group \(|W_{g}|=1000\), and the reliability requirement \(P_{req}=0.999\), while changing the target tag ratio from 0.2 to 0.8 by 0.2. Then, we set the number of groups \(G=21\) and the group interval \(r=10\) in Figure 6(a), set the number of groups \(G=41\) and the group interval \(r=20\) in Figure 6(c). We find that A-Search and G-Search always perform well. In Figure 6(a), when the target tag ratio \(\lambda=0.4\), the time cost of B-Search, G-Search, and A-Search is 9.59 s, 9.39 s, and 9.23 s. Compared with B-Search and G-Search, the time cost of A-Search reduces by 3.75% and 1.69%. In Figure 8, we set the number of local tags in each group \(|L_{g}|=2000\), the number of wanted tags in each group \(|W_{g}|=1000\), and the target tag ratio \(\lambda=0.3\).