## 5 Performance Analysis
### Random Topology  
In the second simulation, the performance metrics of the original DD (OPP) and the proposed RA were compared in a random topology with diverse error rate at 0%, 5%, 10%, 15%, and 20%. Figure 6: The average transmission delay for each error rate in grid topology (0%, 5%, 10%, 15%, 20%). Figure 7: Performance comparison for each error rate in random topology (0%, 5%, 10%, 15%, 20%). (a) Packet delivery rate, (b) Protocol overhead, (c) Total number of packets. Figure 7 shows the data delivery rate, the protocol overhead and the total number of packets for each error rate with the random topology. Compared to the grid topology, the data delivery rate of OPP decreased more quickly with random topology as the error rate increased. From our analysis, the data delivery rate tends to be affected by errors due to the irregular distance among neighbor nodes. Because the irregular distance leaves few candidate routes in addition to the failure node, the number of alternative routes also decreases. As a result, the data delivery rate of OPP is very low with the random topology. In the random topology, RA shows a poor data deliver rate compared to the grid topology. However, RA shows still better data delivery rate than OPP as shown in Figure 7(a). The protocol overhead of both OPP and RA with random topology is four times less than that with the grid topology. Since the number of nodes increases and the distance among neighbor nodes gets random, the number of control packets also increases. The number of data packets in the network decreases with increasing error rate, as shown in Figures 7(b) and 7(c). Furthermore, the number of control packets with the random topology increases with an increasing number of nodes, because the distance among candidate nodes are different. In the random topology, the total number of packets was increased to three times more than that with the grid topology. As the total number of packets increases and the data delivery rate decreases, the protocol overhead increases consequently. RA shows a higher total number of packets than OPP in Figure 7(c). This results from the re-transmission of packets that provide reliable communication through the re-route scheme. Nevertheless, the protocol overhead of RA shows better performance as  
\begin{table}
\begin{tabular}{|c|l|l|l|l|l|l|} \hline Error rate & \multicolumn{2}{c||}{Delivery rate} & \multicolumn{2}{c|}{Overhead} & \multicolumn{2}{c|}{Total packets} \\ \cline{2-7} (\%) & OPP(\%) & RA(\%) & OPP & RA & OPP & RA \\ \hline No error & 100 & 100 & 274 & 274 & 49,481 & 49,908 \\
5 & 55 & 98 & 489 & 277 & 48,818 & 50,218 \\
10 & 34 & 95 & 8  
the error rate increases. This proves that proposed RA maintains reliable communication and does not affect the data delivery rate regardless of error rates or topologies. Table 4 shows all of the metrics in the simulation results. Figure 8 shows the average transmission delay time for each error rate in a comparison between OPP and RA. The average transmission delay of RA is also smaller than that of OPP for all error rates with the random topology. Compared with the grid topology, as time increases, OPP and RA show more delay at a certain time, as shown in Figure 8. In particular, the maximum average transmission delay with OPP is seen more frequently over all error rates. The lossy situation occurs more frequently with random topology due to its random characteristics. The average transmission delay of RA also exceeds that of the grid topology. However, compared to OPP, RA shows small average transmission delay with the random topology. In the random topology, less data is successfully sent to the sink node compared to grid topology. The average transmission delay occurs, because the distance between neighbor nodes is different from a random deployment of nodes. This random distance tends to affect the gradient set up for each route when an error occurs at a node. As a result, OPP shows a higher average transmission delay at every error rate compared to OPP in the grid topology.