## 5 Performance Analysis  
### Grid Topology  
In the first simulation, the performance metrics of original DD (OPP) and the proposed RA were compared in a grid topology with error rates of 0%, 5%, 10%, 15%, and 20%. Figure 5 shows the simulation results in the grid topology. From Figure 5(a), as the error rate increases, the data delivery rate decreases in both algorithms. Both OPP and RA show 100% delivery for the stable condition (error rate, 0%). However, when the error rate increases to 20%, the data delivery rate of RA is four times better than OPP. The reason is RA used the air time cost and route failure information for the current wireless link. That is, RA can adjust in the lossy situation.  
Figure 5: Performance comparison based on error rate in grid topology (0%, 5%, 10%, 15%, 20%). (a) Data delivery rate, (b) Protocol overhead, (c) Total number of packets.  
The protocol overhead of RA is also smaller than OPP. Figures 5(b) and 5(c) show the simulation results. The ratio of control packets over data packets is shown in Figure 5(b) and the total number of packets is shown in Figure 5(c). As the error rate increases in OPP, the number of control packets increases rapidly in inverse proportion to the number of data packets. If the route is broken during data transmission period, the data can be sent back to the sender. When the sender receives the packet from the receiver node again, the sender assumes the route is a loop. Removal of the packet loop relies on negative reinforcement.  
The protocol overhead of OPP increased more as the number of control packets and transmission failures increased. RA maintains low protocol overhead compared to OPP, RA does not affect the error rate significantly in spite of increasing the error rate with RA. RA keeps a higher data delivery rate at every error rate. In addition, the air time cost and the fast re-route scheme are used to provide reliable communication with RA. Additional control packets do not need to be sent to remove the loop. RA re-routes to an alternative path after a failure. For this reason, although the total number of packets with RA is larger than that with OPP, the data delivery rate and the protocol overhead of RA are better than OPP. Table 3 summarizes the results of the simulations.  
Figure 6 describes the average transmission delay for each error rate. The average transmission delay was measured by successfully delivered data from a source to a sink as the time elapsed during simulation. When the data matches the interest at a source node, the source node sends data to a sink node at every five seconds.  
\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 & 69 & 69 & 14,715 & 14,787 \\
5 & 78 & 97 & 93 & 70 & 14,516 & 14,897 \\
10 & 53  
The average transmission delay of RA is quite smaller than that of OPP for all error rates. As the error rate increases in lossy WSNs, OPP suffers from a data loss. In this case, OPP cannot send data to a sink unless the route is set up again by interest propagation. When data transmission fails, the maximum delay time follows the interest propagation cycle. In this paper, we used 60 seconds as the interest propagation cycle. Since RA is able to re-route using the air time cost and route failure information during data transmission period, RA shows a small average transmission delay. However, if the error rate is above 15%, the alternative routes decrease, and the average transmission delay increases slightly. The results are shown in Figure 6.