## 3 Ferry Node Ranking Clustering Algorithm (FNRCA)
### Performance Evaluation of FNRCA against other Algorithms  
We looked into comparing our algorithm with other state of the art ones under not exact but similar operating conditions. We are using a random uncontrolled path, but in the literature, some of the well-known algorithms we found such as [40]) are using controlled paths for the ferry to follow. In addition, there are other algorithms which are using multiple mobile sinks such as in [19,20,40] while we are using only one mobile object which is the ferry as a temporary sink. Moreover, we are limiting the multi-hoping in our algorithm to one hop count while the other algorithms, especially the ones using rendezvous approaches [19,20], are using multi-hopping (one or more hop count) combined with the use of mobile elements to collect data. Nevertheless we have considered further analysis and comparisons against two recent algorithms [21,22]. In these two recent algorithms the authors proved that their proposed algorithms outperformed other existing ones. In order to compare our algorithm with these two, we adapted their used parameters shown in the Table 6 in our simulation. From Figure 5, it is shown how FNRCA outperformed WRP [21] and Charalampos [22] in terms of network lifetime as the last node in FRNCA died after 1200 s compared to1000 in WRP and 1050 in Charalampos. In WRP 50% of the nodes died after 4500 s, in Charalampos after 4800 s while in FRNCA 50% of its nodes died after 6000 s. This can be mostly contributed to the use of multi-hop communication in WRP and Charalampos which will consume more energy in general and will results in a fast depletion of energy on cluster heads closer to the ferry path. However, in our algorithm checkpoints are just locations where the ferry will stop to collect data from cluster heads that belong to its virtual grid where each cluster head is just one hop count from the checkpoint position they are associated with. Charalampos achieved slightly better results than WRP since it selects cluster heads with higher energy as rendezvous points when using nodes with different initial energy values. However as can be seen from Figure 6, similar results are achieved by both WRP and Charalampos when using the same energy value to start with. In both cases, FNRCA outperformed the two algorithms when using same or different initial energy values. In addition, comparing the graph for FNRCA in Figures 5 and 6 shows minimal changes in its performance regardless of whether the same initial energy value was used by all nodes or uniformly distributed ones were used. This is mainly due to the fact that FNRCA incorporates current energy values in selecting and rotating cluster heads and minimizes multi-hop communication.  
Figure 4: Number of checkpoints _vs._ round trip time.  
**Figure 5**: Network Lifetime for FNRCA, WRP and Charalampos using different initial energy values.  
\begin{table}
\begin{tabular}{c} \hline
**Notation** \\ \hline N = 200 \\ Initial node energy, Eo = uniformly selected for the nodes from 50–100 J / node \\ Area = 200 \(\times\) 200 \\ \# Checkpoints = 25 \\ Packet size = 30 Bytes \\ Data Rate = 40 Kbps \\ Sensing Radius : r = 20 m \\ Ferry speed = 1 m/s \\ \hline \end{tabular}
\end{table}
Table 6: Parameters used in the simulation to compare FNRCA to [21,22].  
Figure 6: Network Lifetime for FNRCA, WRP and Charalampos using the same initial energy values.