## 5 Performance Evaluation
### Comparison of BSMH and Other Benchmarks
#### 5.4.6 Maximum Packet forwarding Ratio  
The maximum packet ratios caused by the protocols are shown in Figure 18. As shown, our protocol (especially with high values of \(\epsilon\)) strongly outperforms the other ones. Specifically, the maximum packet forwarding ratio caused by BSMH for all settings of \(\epsilon\) is smaller than those caused by LVGR, EDGR and GPSR in all topologies excepting topology 6 in 1-n communication. EDGR and LVGR attain the second-best and third-best performances in most of the cases, and GPSR shows the highest maximum packet forwarding due to the perimeter routing nature. With \(\epsilon=1.2\), BSMH results in the maximum packet forwarding ratio which is less than 73% that of LVGR, 81% and EDGR and 64% that of GPSR, in all 1-n communication topologies. In the best cases, the maximum packet forwarding ratio caused by BSMH is smaller 41%, 32% and 27% those of LVGR, EDGR and GPSR, respectively. Regarding the n-n communication, BSMH with \(\epsilon\) reduces the maximum packet forwarding ratio by the factors of 0.51, 0.52 and 0.44 compared to LVGR, EDGR, and GPSR, respectively. In the best cases, the maximum packet forwarding ratio resulted by BSMH is smaller than 0.18, 0.16 and 0.17 times those of LVGR, EDGR, and GPSR, respectively. The maximum packet forwarding ratio caused by BSMH with \(\epsilon=0.5\) is always smaller than 96% that of LVGR, 68% that of EDGR (in 5/6 cases), and 84% that of GPSR in the 1-n communication. With respect to the n-n communication,  
Figure 17: The ratio of the number of packets successfully delivered to the total number of packets sent. (a) 1-n communication. (b) n-n communication. the maximum packet forwarding ratio caused by BSMH with \(\epsilon=0.5\) is always smaller than 60% that of LVGR, 70% that of EDGR and 63% that of GPSR. When reducing \(\epsilon\) to 0.3, BSMH outperforms all the existing protocols regarding all topologies in the n-n communication and 5/6 cases regarding the 1-n communication. Regarding Topology 6 in 1-n communication, it can be seen that BSMH with \(\epsilon=0.3\) shows the worst performance and BSMH with \(\epsilon=0.5\) shows the third-worst performance among all the protocols. This phenomenon can be explained as follows. First, as this topology consists of many small holes, the diversity of routing paths determined by the other protocols (i.e., LVGR, EDGR, GPSR) is increased. Therefore, the performance attained by the other protocols in this topology is better than those attained by the same protocols in other topologies. Secondly, as the spaces between the holes in this topology are small, the scale factors used in the homothetic transformations for determining the Euclidean routing paths in BSMH is limited. In other words, the diversity of routing paths determined by BSMH is degraded in Topology 6. Consequently, BSMH with small values of \(\epsilon\) cannot improve load balance in comparison with other protocols. Another observation is that the maximum packet forwarding ratios of all protocols in n-n communication are smaller than those in 1-n communication. This can be seen by comparing Figure 18a,b, where the values plotted in Figure 18b are much smaller than those plotted in Figure 18a. Moreover, the performance gaps between BSMH and the other protocols regarding n-n communication is larger than those regarding 1-n communication. This phenomenon can be explained by the so-called hotspot problem caused by the high traffic load around the destination. To facilitate the understanding, we also plot the distribution of packet forwarding ratios of all nodes in Figure 19. It can be seen that the span of the distributions caused by BSMH in both 1-n and n-n communication are much larger than those caused by the other protocols. This result means that the number of sensors participating in data forwarding in BSMH is much more than those in the other protocols. Moreover, the height of the distribution attained by BSMH is much smaller than those of the other protocols.