# An Efficient Relayed Broadcasting Based on the Duplication Estimation Model for IoT Applications
## 4 Simulation Study
### A Performance Comparison of the Various Flooding Mechanisms
#### 4.3.2 The Number of Duplicate Frames  
We investigated the performance in terms of redundancy. As shown in Figure 11a, \(\overline{F}_{dup}\)s in all of the mechanisms linearly increased as \(N_{node}\) increased. This result was very similar to \(\overline{T}_{dis}\) and implies that the transmission of duplicate frames is the main reason for the increase in \(\overline{T}_{dis}\). More specifically, as \(N_{node}\) increased from 60 to 140, the \(\overline{F}_{dup}\)s of BASE and PBF increased approximately from 3800 to 5300 and from 10,800 to 29,900, respectively. Considering that the source node generates only 1000 frames, the nodes in BASE and PBF received many more duplicate frames by up to 5 and 30 times, respectively. Please note that in the case of BASE, even the increase in the number of duplicate frames (Figure 11a) not only increased the traffic dissemination time (Figure 10b) but also degraded the reliability (Figure 10a), thus confirming the necessity of duplication suppression in the flooding. Serious redundancy significantly decreased in DRBF\({}_{\text{RQ}}\). Compared to PBF, DRBF\({}_{\text{RQ}}\) decreased \(\overline{F}_{dup}\) by up to 6.4 times. The \(\overline{F}_{dup}\) of CBF was the smallest and comparable to that of DBF, but they attained smaller \(\overline{F}_{val}\)s than DRBF\({}_{\text{RQ}}\), i.e., CBF and DBF cannot assure the high reliability of flooding, despite their lower level of redundancy, compared to DRBF\({}_{\text{RQ}}\).  
We further observed the redundancy in a different aspect. Figure 11b shows the distribution of the number of duplicate frames received in all of the nodes (denoted as \(N_{dup}\)) in BASE, DRBF, and DRBF\({}_{\text{RQ}}\)  
Figure 11: The performance comparison of the flooding mechanisms in terms of (**a**) the number of duplicate frames (\(\overline{F}_{dup}\)) and (**b**) the distribution of number of the duplications in all of the nodes.  
Figure 10: The performance comparison of the flooding mechanisms in terms of (**a**) the number of valid frames (\(\overline{F}_{val}\)) and (**b**) the dissemination time (\(\overline{T}_{dis}\)).  
In Figure 11b, the lower and upper bars indicate the 1 st and 99 th percentiles, respectively, and the bottom, top, and middle line of the box represent the 25 th and 75 th percentiles, and the median value, respectively. In the case of BASE, \(N_{dup}\) was was distributed over a higher and wider range than DRBF and DRBF\({}_{\text{RQ}}\); when \(N_{node}\) was 60, the 25 th and 75 th percentiles were 4 and 7, respectively, and they extended to 6 and 10 when \(N_{node}\) was 140. On the other hand, DRBF and DRBF\({}_{\text{RQ}}\) moved the distribution of \(N_{dup}\) down, as well as its median value. For example, the 75 th percentile of \(N_{dup}\) was 4 and 6 in DRBF when \(N_{node}\) was 60 and 140, respectively, which were equal to those of the 25 th percentile in BASE. In DRBF and DRBF\({}_{\text{RQ}}\), the difference between the 25 th and 75 th percentile was at least 2. Moreover, we found that the distribution of \(N_{dup}\) in DRBF\({}_{\text{RQ}}\) when \(N_{node}\) = 60 was mostly identical to that in DRBF when \(N_{node}\) = 140. This implies that the re-queuing scheme in DRBF\({}_{\text{RQ}}\) has an effect similar to virtually increasing the number of active nodes so that the frame delivery failure can be recovered by the more of adjacent nodes.