# Optimized Dynamic Deployment of UAVs in Maritime Networks with Route Prediction
## 3 System Modeling
### Time-Delay Model  
Due to the limited computational resources of each device, when the computational resources of satellites and base stations are insufficient to meet the computational needs of users, UAVs are required to perform auxiliary computations. However, a non-negligible delay is generated in the process of providing communication and computation services to users, so this section focuses on the delay model in the maritime communication scenario. Assuming that at the \(t\)-th time slot, if the maritime user \(n\) is within the communication coverage of both the satellite and the base station, and both of them have sufficient computational resources, the user equipment will prioritize establishing a communication connection with the satellite, if the satellite resources are insufficient, it will choose the base station to communicate; if the base station also fails to satisfy the demand, the equipment will try to communicate with the nearest UAV. When the mission ends, the device will recover the amount of computation required for that user's mission. In marine environments, the flight delay and transmission delay are affected by environmental factors such as wind speed, humidity, and airflow, which are assumed to be represented by a discount factor \(\omega\in(0,1)\). Additionally, the complexity of the computational task is represented by a factor \(k\left(k>0\right)\). When the amount of computation required \(a_{n}\) for a user task is less than the computational power \(a_{\text{leo,axa}}\) available to the satellite, the user device will establish a communication connection with the satellite. Assume that the channel transmission rate between the satellite and user \(n\) is \(r_{\text{leo,n}}(t)\). The amount of data to be transmitted by user device \(n\) is \(q_{\text{leo,n}}\), and the amount of task data that can be processed by the satellite per second is \(f_{\text{Leo}}\). Then the total delay of the satellite can be expressed as Equation (14):  
\[d_{\text{Leo,n}}(t)=d_{\text{trans leo,n}}(t)+d_{\text{comp leo,n}}(t), \tag{14}\]  
where the task transmission time \(d_{\text{trans leo,n}}(t)\) and computational delay \(d_{\text{comp leo,n}}(t)\) can be expressed as Equations (15) and (16), respectively:  
\[d_{\text{trans leo,n}}(t)=\frac{q_{\text{Leo,n}}}{\omega\cdot r_{\text{Leo,n}}( t)}, \tag{15}\]  
\[d_{\text{comp leo,n}}(t)=\frac{k\cdot q_{\text{Leo,n}}}{f_{\text{Leo}}}, \tag{16}\]  
Similarly, when the amount of computation required \(a_{n}\) for a user task is less than the computational power \(a_{\text{tbs,ava}}\) available at the base station, the user device will establish a communication connection with the base station. The total delay between the base station and the associated user \(n\) can be expressed as Equation (17), where the task-transfer time \(d_{\text{trans tbs,n}}(t)\) and computational delay \(d_{\text{comp tbs,n}}(t)\) are given by Equations (18) and (19), respectively:  
\[d_{\text{tbs,n}}(t)=d_{\text{trans tbs,n}}(t)+d_{\text{comp tbs,n}}(t), \tag{17}\]  
\[d_{\text{trans tbs,n}}(t)=\frac{q_{\text{tbs,n}}}{\omega\cdot r_{\text{tbs,n}}( t)}, \tag{18}\]  
\[d_{\text{comp tbs,n}}(t)=\frac{k\cdot q_{\text{tbs,n}}}{f_{\text{tbs}}}, \tag{19}\]  
When the amount of computation required \(a_{n}\) for a user task is less than the computational power \(a_{\text{m,ava}}\) available to UAV \(m\), the user device will establish a communication connection with UAV \(m\).