# Transfer-Efficient Face Routing Using the Planar Graphs of Neighbors in High Density WSNs
## 5 Performance Evaluation
### Simulation Results  
Figure 10 shows a graph comparing the time at which the message was forwarded from the source to the destination according to the number of deployed nodes. With GFG, as the number of deployed nodes increases, the number of nodes to be traveled increases because the number of nodes constituting a face increases. Thereby, the transfer time increases gradually in proportion to the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Simulator & Qualnet 4.0 \\ The radio range of the sensor node & 50\(\sim\)250 m (increased by 20 m) \\ The number of sensor nodes & 200\(\sim\)1500 nodes (increased by 100 nodes) \\ Node placement & Random \\ Network size & 1000 \(\times\) 1000 m\({}^{2}\) \\ Network model & unit disk graph \\ Routing protocols & GFG, SBFR, TEFR \\ Planar graph & [PERSON] graph \\ Simulation time & 100 s \\ Number of Simulation Executions & 100 times \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation environment. Figure 11: Transfer time according to radio range (deployed nodes: 500). Figure 10: Transfer time according to the number of deployed nodes (radio range: 100 m). increased number of nodes. With SBFR, since a message is sent directly to the most remote node within radio range, even if the number of nodes increases, the time for forwarding a message is constant. However, since it performs planarization on all nodes within 2-hop range of a message transfer node, as the number of nodes increased, the computation time increased, resulting in the message transfer time, which includes the computation time, becoming longer. Since TEFR sends a message directly to the most remote node within radio range and the generation of the planar graph is performed in a distributed manner at the neighbor node, the increase in the number of nodes has little effect on the transfer time. From the experimental results, we can confirmed that the transfer time of TEFR was hardly affected by an increase in the number of nodes. Figure 11 shows a graph comparing the transfer time from the source to the destination according to changes in radio range. With GFG, even if the radio range is widened, it is necessary to sequentially travel along the nodes connected with short edges regardless of the radio range. Thus, the transfer time did not decrease even when the radio range was expanded. With SBFR, as the radio range increases, a message can be directly sent to a node located at a longer distance, thereby reducing the transfer time. However, as the radio range is widened, the number of nodes within radio range increases and the construction time of the planar graph increases accordingly. As the radio range exceeds a certain distance, the wider the radio range, the longer the transfer time. With TEFR, even if the number of nodes to be planarized increases due to an increment in radio range, the transfer time is not significantly affected because planarization is distributed to the neighbors of the message transfer node, and the message can also be sent directly to the node farthest away. As a result, as the radio range increased, the transfer time decreased. Figure 12 shows the transfer time of each face routing according to the ratio of the node that can forward a message directly to the remote node in an experiment to consider the power state of the node. In practice, SBFR does not take into account the power state of the node, but in order to compare the transfer time in this simulation, it sends a message sequentially when the message transfer node has less power than the threshold. Since GFG transfers a message sequentially along the face boundary, the transfer times are similar regardless of the proportion of nodes performing direct transmission. However, in SBFR and TEFR, the number of nodes forwarding a message to the remote node also increases as the ratio of nodes capable of direct transmission increases, resulting in a decrease in end-to-end transfer time.