## 3 Cluster-Disjoint Multipath Routing Protocol
### Grid Cluster Construction
RMR is a scheme to achieve high reliability based on radio-disjoint multipath routing. In particular, it increases the network lifetime by exploiting different paths for each packet transmission using guardbands located between paths. In Section 4.1, we explain the simulation environments and evaluation factors. The simulation results according to the end-to-end distance are provided in Section 4.2, and the results according to the single-hop transmission success ratio are provided in Section 4.4. ### Simulation Environments

We simulate and analyze the existing protocols and the proposed scheme using the NS-3 simulator. Table 1 provides the detailed simulation environments of our simulation. The nodes are placed in a terrain of a 1000 m \(\times\) 1000 m area. A total of 100 nodes are placed in the form of a grid, and the remaining 900 nodes are deployed randomly. The performance of each node follows the MICA2 specification. The transmit and receive power consumption values of the node are 24.92 and 19.72 mJ per one byte, respectively. The simulations are performed 30 times, and the graphs represent the average result of the simulations. The evaluation factors and terms are described as follows:

* End-to-end distance is defined as the linear distance between the source and the sink. * Single-hop transmission success ratio is defined as the average transmission success ratio between neighboring nodes. Figure 3: An Example of Cluster-disjoint Multipath Packet Transmission. First packet arrival time is defined as the time between the source detecting the event and the arrival of the first packet sent to the sink. * End-to-end transmission success ratio is defined as the number of packets received by the sink relative to the number of packets sent by the source. * Energy consumption is the sum of the energy consumption of the nodes that participated in the packet transmission process. ### Simulation Results by End-to-End Distance

In this section, we present the performance evaluation results while varying the end-to-end distance under the single-hop transmission success ratio of 90% (from 85% to 95%) to investigate its effect on the first packet arrival time, end-to-end transmission success ratio, and energy consumption. Figure 4 shows the first packet arrival time of each protocol according to end-to-end distance. FD-AOMDV has a slower first packet arrival time compared to RMR and the proposed scheme because they both perform path establishment through RREQ message transmission from a source node that detects the event to the sink node and the RREP reply from the sink node. RMR and the proposed scheme are relatively fast due to the immediate computation and route establishment of the source node and the grid cluster head node without the route establishment process based on RREQ and RREP messages. The proposed scheme exploits a pre-calculated grid cluster structure without complex computation at the cluster head and immediately forwards the packet by branching as multipaths as required to satisfy the end-to-end transmission success ratio. RMR does not exploit RREQ or RREP messages; however, it requires additional computational time to construct multipaths. Therefore, the proposed scheme has a slightly faster first packet arrival time compared to RMR. Figure 5 shows that the end-to-end transmission success ratio of each protocol depends on the end-to-end distance. Each protocol could construct multipaths to achieve the required end-to-end transmission success ratio. However, in case of FD-AOMDV, since it focuses on the node-disjoint of each path, the transmission success ratio is significantly lower than that of other schemes due to collisions and interference between each path in simultaneous transmission exploiting multipaths. For the other two schemes, if the end-to-end distance is short, a sufficient number of paths can be constructed to achieve the required end-to-end transmission success ratio.