## 2 Modeling and Formulation
### Air-R
Figure 7c, d illustrates the number of the replaced failed nodes utilizing the high capability of the _BS_ in detecting the failed node (based on the calculation and analyzing the incoming data from the nodes through a continuous synchronized data exchange between _BS_ and Air-R on both network sizes). Figure 7c shows the number of successful nodes replaced in the small network. Particularly, the Air-R starts to receive the replacement requests from the _BS_ at the beginning, successfully replaces two failed nodes, and receives more replacement requests until no more requests are acquired (or it needs to come back to the _BS_). Similarly, Figure 7d shows the number of successful nodes replaced in the large network. The Air-R successfully replaces three failed nodes in the first 50 min (which continues to increase), and detects the failure to exploit the replacement task until no more requests are received from the _BS_. This condition is due to the early and fast detection of the network failure, which leads to the sustainability and high performance of the network. * _Network performance._ This parameter is the average value expressed in minutes between the network start up and the first failed node found in the network. Network performance refers to the number of nodes that have been replaced to apply network sustainability, as shown in Figures 5-7 (when the failure is detected before it affects the network). * _Air-R travel distance._ This parameter captures the amount of distance spent by the Air-R in flying around the network. The Air-R travel distance highlights how our proposed field partition is efficient in reducing the travel distance for the Air-R and decreasing the Air-R effort to cover the monitoring field for the replacement of the failed nodes. In particular, the adoption of the path selection (based on the TSP solution) performs the best for Air-R, as shown in Figure 4:3

Figure 4:4 Network statistics’ average for small and large networks utilizing the SBR technique: (a) finding failed nodes in a small network; (b) finding failed nodes in a large network; (c) successful node replacement in a small network; (d) successful node replacement in a large network. In the final analysis, we investigate how the Air-R path influences the movement distance to reduce the Air-R effort. Consequently, the Air-R replaces the failed nodes before the problem extends, which affects network sustainability. Figure 8 shows the movement average for the Air-R, which is always the lowest, most stable, and most constant when utilizing the SBR technique in both network sizes. In the SBR technique, the _BS_ selects the closest Air-R to the sector that presents failure. The Air-R then flies to replace the failed nodes in the sectors. The highest performance is achieved, and the travel distance for Air-R is reduced. ## 4 Conclusions

In this study, we propose a sensor replacement technique for R-WSN using Air-R, called SBR. The _BS_ receives recharging requests from nodes in the monitoring field, analyzes these requests, and checks which node sends numerous abnormal recharging requests. The Air-R is then sent to replace the failed nodes with new functional ones. This study aims to (i) guarantee the sustainability of the R-WSN monitoring field without affecting any part; (ii) rapidly detect the failed node in sectors on the R-WSN using the _BS_ capabilities in processing the data, to achieve the highest performance for the replacement of the failed nodes; and (iii) minimize the Air-R movement distance through the new field-dividing mechanism that leads to the fast replacement task. The proposed solutions succeed in guaranteeing the sustainability of the R-WSN monitoring field. We believe that the proposed comparative analysis will be helpful in various uses of WSN for monitoring and collecting data about environmental activities. In our future work, we will study the performance of utilizing Air-R to deploy fully functional nodes in non-covered places in the sensing field.