## 3 System Model
### ARIMA-Based Residual Energy Prediction Model  
In the rescue phase, some nodes may be required to stay in the air for a period of time, or flight speed is relatively slow, which will cause nodes to consume less energy in the marginal area, but consume a lot of energy in the central region, i.e., energy imbalance. Eventually, some central nodes die early, leading to sparse network topology, and further decreasing packet delivery rate. In order to clarify the problem, we use Figure 1 as an example, which shows UAV nodes and communication links in UANETs. Source nodes \(i,b,c\) want to send packets to the destination node \(d\) at different time slots. Then, packets will be forwarded through nodes \(j\) and \(k\) successively and finally reach the destination node \(d\). Hence, relay nodes \(j\) and \(k\) will take on more communication tasks, leading to the nodes becoming congested and more likely to run out of energy. Assuming node \(j\) is on the verge of death, but node \(i\) does not receive the latest hello packet from the node, if the node still sends packets to node \(j\), it will cause packet loss. Therefore, we take energy into consideration when selecting the next hop to address the energy imbalance problem. In our scenario, the influence that the external environment, the weather, and some unimportant factors have on energy are ignored. The energy consumption of UAVs is mainly divided into the following three parts: flight energy consumption, send-packet energy consumption, and receive-packet energy consumption. Nodes move at the same velocity magnitude, but in random directions, so the flight energy consumption is basically proportional to the time. The residual energy of node \(j\) after receiving packets from nodes \(i,b,c\) and sending packets to node \(k\) during a hello interval is denoted as follows. \[E_{j}^{res}(t_{1})=E_{j}^{res}(t_{0})-m\cdot P_{size}\cdot\left(E_{tx}+E_{fs}d_ {jk}^{2}\right)-n\cdot P_{size}\cdot E_{rx}-E_{fly} \tag{3}\]  
where \(E_{j}^{res}(t_{0})\) is the residual energy of the node at the last hello moment \(t_{0}\). \(E_{j}^{res}(t_{1})\) is the residual energy of the node at the current hello moment \(t_{1}\). \(E_{fly}\) is the flight energy consumption during a hello interval. \(E_{rx}\) and \(E_{tx}\) are the energy consumption when transmitting and receiving a packet, respectively. \(\varepsilon_{fs}d_{ij}^{2}\) is the required energy loss in the free-space model; the energy dissipation coefficient of the circuit amplifier is 2. Meanwhile, each node records its residual energy sequence during the last ten hello intervals and formats the energy sequence in the hello packet header. For example, the residual energy sequence of node \(j\) is represented as \(\mathbf{E}_{j}=\left[E_{j}^{\text{res}}\left(t_{1}\right),E_{j}^{\text{res}}\left( t_{2}\right),\cdots,E_{j}^{\text{res}}\left(t_{10}\right)\right]\). Each node periodically broadcasts its energy sequence to the neighbor nodes by hello packets. For the sake of avoiding nodes dying early due to packet loss, each node uses the ARIMA model to predict neighboring nodes' residual energy by receiving neighbors' energy sequences. The ARIMA model is a time-sequence analysis model which can use historical data to predict future values. It has flexible and excellent forecasting performance and lightweight computational cost. Moreover, the reason we used the ARIMA model is  
Figure 1: UAV network topology and communication link. that the energy of UAVs is affected by many factors, so the variation pattern of energy consumption is neither stationary nor purely linear or non-linear. Some statistical prediction methods, such as the autoregressive (AR) model, the moving-average (MA) model and the ARMA model, cannot adapt to our scenario. However, the ARIMA model can be applied in a non-stationary time sequence. Due to UAVs' residual energy sequence being non-stationary, firstly, we should preprocess the residual energy sequence when a node receives a hello packet from a neighboring node.