## 6 The Extensions of EAR2M
nodes send the data of the source with the information of the \(S_{speed\_fp}\) to each of the other flooding points (p2, p3, and p4 in Figure 4a) by unicasting. Similarly, the sensor node the nearest to each flooding point and belongs to the \(EA\) receives the data from the sources. Thus, the sensor nodes flood the received data of the source within the \(EA\) using all flooding points. Furthermore, all sensor nodes in \(EA\) receive and flood the data only once regardless of the initial flooding nodes. As a result, the mobile sink in \(EA\) can receive the data from the source node. Figure 3 shows that the source node forwards its data to four flooding points, and the nodes at the flooding points concurrently flood the data within the \(EA\). The number of flooding points greatly influences the performance of EAR2M. Thus, we compare the performance of EAR2M for the number of flooding points in terms of the energy consumption and the deadline success ratio. In order to reduce the energy consumption of data relaying between flooding points, the second approach, EAR2M_E allows the flooding points to relay the data packet to another flooding point. As described above, EAR2M delivers data packets from a source to flooding points for flooding the packet into the \(EA\). The nodes on the flooding point share the data packet and start the data flooding. In the EAR2M_E, in order to minimize the energy cost for sharing the data packet among the flooding point, the adjacent nodes on the flooding points share the data packet directly, as shown in Figure 4b. The direct communication between the adjacent flooding points could reduce the cost for data sharing more greatly than EAR2M_R. Although the farthest distance of the data dissemination is longer, the summation of the data dissemination distance could be shorter and EAR2M_E could reduce the energy consumption. As with EAR2M_R, EAR2M_E synthetically calculates the data delivery speed to multiple flooding points. EAR2M_E calculates the data delivery speed \(S_{sped\_fp}\) to the farthest flooding point _fp_ via multiple flooding points as follows:  
\[S_{sped\_fp}=\frac{d(src,p1)+\sqrt{2}d(p1,fp)}{T_{setdeadline}-T_{floading\_ n}}. \tag{9}\]  
After EAR2M_E determines the locations and number of flooding points, it calculates the data delivery speed \(S_{sped\_fp}\) using Equation (9). The source node sends its data toward the closest flooding point. The node on the closest flooding point receives the data packet and relays it toward the other flooding points except the farthest flooding point. For data transmission toward the farthest flooding point, the node on one of the other flooding points relays the data packet. The total distance by the unicasting in EAR2M_R and EAR2M_E is calculated as followings:  
\[ \begin{split} TD\_R&=(d(src,center)-r)+2\sqrt{2}r+ 2r\\ &=d(src,center)+(2\sqrt{2}+1)r,\\ TD\_E&=(d(src,center)-r)+3\sqrt{2}r\\ &=d(src,center)+(3\sqrt{2}-1)r,\end{split}  \tag{10}\]  
where \(d(src,center)\) is the distance between the source node and the center point of the expected area and \(r\) is the radius of the expected area. According to the above equations, the farthest unicasting distance of EAR2M_R is less than that of EAR2M_E and the summation of the unicasting distance of EAR2M_R is greater than that of EAR2M_E. In our opinion, we expect that EAR2M_R and EAR2M_E have a trade-off between the transmission delay and the energy consumption, as mentioned in several relevant papers [16; 17]. Thus, we prove the trade-off through the experimental results in Section 7.4.