# Energy and Distance-Aware Hopping Sensor
## 3 Simulation Results and Analysis
In contrast, simulation results with a weight close to 1 that only takes into account the hopping capability will be the slowest. However, in a rearrangement of the hopping sensor nodes, it cannot be determined whether considering only the distance is desirable in order to reduce the recovery time. In fact, it is also important to consider the energy for movement, since sensor nodes are inherently energy-limited. Therefore, various simulation results below are mandatory to see how these weights affect the results. As shown in Figure 11, sensor nodes in a specific cluster continuously collecting data lead to a failure (yellow marked). In order to recover such a sensing hole, a scenario in which the hopping sensors move is repeated over time. Figure 13 shows the number of movable sensors over the entire network according to the simulation time. A fault in a hopping sensor node is not simply determined by the depletion of energy due to collecting data. If the sensor is impossible to move due to frequent movement, it is also regarded as a fault of the hopping sensor node. The number of surviving nodes is the largest when only mobility (energy for movement) is considered. However, we cannot conclude that considering the possibility of movement is the best for sensing hole recovery. The following results supplement this explanation. Figure 12: The average recovery time according to weight \(w\). In Figure 14, the number of REQs, which is a hopping sensor movement request message for a sensing hole recovery, is analyzed according to the simulation time. Briefly, considering the energy, the frequency of occurrence of REQ is decreased. In contrast, the frequency of REQ is increased considering distance only. The reason for this is as follows:  
First, the occurrence of REQ generally means that a sensing hole is detected. If a node is defective due to continuous data collection in a specific cluster zone, it is possible to speed up the recovery time considering only the distance. However, since the sensing hole appears again after the fast recovery, the number of REQs should be increased. Second, from a different point of view, there is a possibility that defects may occur as the sensor moves, since only the distance is taken into consideration and the energy is not considered. That is, a new REQ may be generated again if the number of available sensors is less than the number of sensors requested by the previous REQ. It is also worthy to note that the definition of the sensing hole means that there are less than a predetermined number of sensors in the cluster zone and does not mean that there is no sensor for data collection. Therefore, it cannot be concluded that the fast recovery of a sensing hole is the most important, considering only the position. That is, selecting a sensor that can survive longer even if the recovery time is little slower and rearranging it will be one of the new approaches. Because of the limited energy of the wireless sensor node, relocation without consideration of the energy may generate more sensing holes and lead to network disconnection. Thus, it is very important to consider the saving of the moving energy of the hopping sensor every rearrangement. Figure 15 shows the average deviation of the residual energy among the deployed member sensor nodes with  
Figure 13: The number of total hopping sensors still alive: (a) A single sensing hole occurred; (b) two sensing holes occurred. the experience of movement, according to the simulation time. The relocation of the member sensor node considering only the shortest distance confirms that the residual deviation of the mobile energy becomes larger as seen in Figure 15. As mentioned above, it can be interpreted that if the residual deviation increases, the ability to recover the sensing hole decreases. Therefore, it can be concluded that a relocation technique considering distance and energy is very important according to importance of recovery time.