## 3 Cluster-Disjoint Multipath Routing Protocol
### Grid Cluster Construction
However, if the required number of paths increases as the distance between the source and sink increases, the RMR cannot have sufficient width for guardband shifting, and the transmission success ratio decreases. In other words, radio-disjoint path construction is achieved, as well as equal utilization of nodes by guardband shifting. However, a larger routing area is required tha \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value(s)** \\ \hline Routing protocols & FD-AOMDV, RMR, Proposed scheme \\ \hline Terrain & (1000 m, 1000 m) \\ \hline End-to-end distance & about 700 m \\ \hline The number of nodes & 1000 nodes Uniform and Random placement \\ \hline Transmission range (m) & 100 m \\ \hline MAC protocol & 802.15.4 MAC \\ \hline MAC layer & CSMA/CA \\ \hline Energy consumption (Tx) & 24.92 m] per 1 byte \\ \hline Energy consumption (Rx) & 19.72 m] per 1 byte \\ \hline Required end-to-end transmission success ratio & 90\% \\ \hline Average Single-hop transmission success ratio & 90\% (85\(\sim\)95\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Environment Setting. scheme to achieve the same performance aspect of the end-to-end transmission success ratio. Therefore, as the end-to-end distance increases, RMR shows a lower transmission success ratio than the proposed scheme. Figure 6 shows the energy consumption of each protocol according to end-to-end distance. Energy consumption is a factor that is directly affected by the transmission and reception of packets between nodes, and the proposed scheme and RMR shows an increase in energy consumption as a result of constructing a large number of paths and forwarding packets as the distance changes. However, as mentioned earlier in the end-to-end transmission success ratio, as the distance increases, RMR no longer constructs a sufficient number of paths when the end-to-end distance exceeds a certain distance, and the total number of packet transmissions is reduced compared to that in the proposed scheme. Therefore, the energy consumption does not increase anymore. In the case of FD-AOMDV, although it might construct a sufficient number of paths as required, the energy consumption is relatively low due to transmission failures caused by collisions and interference during simultaneous transmission over the node-disjoint multipath. Figure 4: First Packet Arrival Time by End-to-End distance. Figure 5: End-to-end Transmission Success Ratio by End-to-End distance. ### Simulation Results by Single-Hop Transmission Success Ratio

In this section, we present the performance evaluation results while decreasing the single-hop transmission success ratio under the end-to-end distance of 1000 m to investigate its effect on the end-to-end transmission success ratio and energy consumption. Figure 7 shows end-to-end transmission success ratio of each protocol according to the single-hop transmission success ratio. For all protocols, the end-to-end transmission success ratio decreases as the single-hop transmission success ratio decreases. In particular, FO-AOMDV further reduces the end-to-end transmission success rate due to collisions and interference between nodes located close to each path. The other two schemes, RMR and the proposed scheme, also show a gradual decrease in the end-to-end transmission success ratio as the single-hop transmission success ratio decreases. However, RMR, which exploits guardband shifting, requires a wider width to construct the same number of paths compared to the proposed scheme. Therefore, when the required number of paths increases due to the decrease in the single-hop transmission success ratio, a sufficient number of paths cannot be constructed and the end-to-end transmission success ratio decreases earlier than in the proposed scheme. Figure 8 shows the energy consumption of each protocol according to the single-hop transmission success ratio. In the case of FD-AOMDV, it would construct a multipath to cope with the decreasing single-hop transmission success ratio.