## 5 EAR2 with Multiple Flooding Points (EAR2M)  
To solve the aforementioned three limitations of a single flooding point, we propose a new protocol called EAR2M that exploits multiple flooding points in EAR2 as shown in Figure 3. Flooding consumes much of the energy of the sensor nodes. Within \(EA\), multiple-point flooding consumes the same energy as single = point flooding. Multiple-point flooding distributively floods at only around multiple points [37; 38], but otherwise, multiple-point flooding allows all nodes in the \(EA\) to receive the flooding data identically to single-point flooding. However, exploiting multiple-point flooding in EAR2M consumes energy when the source forwards its data to the multiple points by unicast. By consuming the data forwarding energy to multiple points, we reduce the flooding time \(T_{f flooding}\) and enhance the reliability of data forwarding to the mobile sink in EAR2M.  
We also carried out a simulation to measure how the distributed flooding at multiple points influences \(T_{f flooding}\). As shown in Figure 2, multiple-point flooding can reduce the flooding time \(T_{f flooding}\) because flooding is distributively performed at multiple points. Figure 2 shows two lines for each flooding point number. The above lines and the below lines show the worst and best values for flooding time in the circle region with radius r, respectively. If the radius of the circular region is large, then when the number of flooding points increases, the worst and best values of \(T_{f flooding}\) are smaller. On the other hand, if the radius of the circular region is small, the worst and best values of the \(T_{f flooding}\) are largely unaffected by the number of flooding points.  
In EAR2M, to provide real-time data routing using multiple flooding points, we recalculate the data forwarding time \(T_{forwarding}\) and the data delivery speed \(S_{speed}\) for each flooding point in Equations (3) and (4) through the flooding time \(T_{f flooding}\) when using multiple flooding points. We use the observed flooding time in Figure 2 as the flooding  
Figure 3: Real-time data routing based on distributed flooding at multiple flooding points.  
time \(T_{flooding\_n}\) when exploiting n flooding points. Thus, Equation (3) is recalculated as follows:  
\[T_{setdeadline}\geq T_{forwarding}+T_{flooding\_n}. \tag{5}\]  
Furthermore, the data delivery speed \(S_{sped\_i}\) to each flooding point \(i\) is calculated as follows:  
\[S_{speed\_i}=\frac{d(src,p_{i})}{T_{setdeadline}-T_{flooding\_i}}. \tag{6}\]  
If the source node selects the number and position of flooding points and calculates the data delivery speed \(S_{speed\_i}\) to each flooding point \(i\), it sends its data with the \(S_{speed\_i}\) information to each flooding point \(i\) through unicast. If the data arrive at each flooding point, the node the nearest to the point in the \(EA\) floods the data within the \(EA\). All nodes in \(EA\) receive and flood the data only once regardless of the initial flooding nodes. If any node receives redundant data, it drops the data. Accordingly, 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 distributively flood the data within \(EA\). 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.