# UAV-Assisted Caching Strategy Based on Content Cache Pricing in Vehicular Networks
## 3 System Model
### Communication Model and Latency Analysis  
This section analyses the communication model and latency for the vehicle user. When the vehicle user is at position \(l\), the rate at which the roadside unit \(R_{m}\), \(m\in\{l,r\}\), transmits content to the vehicle user v is expressed as  
\[R_{m,n}^{RV}(l)=Blog_{2}\bigg{(}1+\frac{P_{m}G_{m,n}(l)}{\sigma^{2}}\bigg{)} \tag{2}\]  
where \(P_{m}\) is the transmit power of \(R_{m}\); \(G_{m,n}(l)\) denotes the channel gain between \(R_{m}\) and \(v_{n}\) for the vehicle user at position \(l\); \(l\in(0,2l)\), \(G_{m,n}(l)=\chi\cdot d_{m,n}(l)^{-\delta}\), \(d_{m,n}(l)\) is the distance between \(R_{m}\) and \(v_{n}\); \(B\) is the channel bandwidth. For communication between UAVs and vehicle users, this paper considers a probability-based air-to-ground communication model consisting of two communication channels: a line-of-sight channel and a non-line-of-sight channel. The probability of line-of-sight transmission is  
\[P_{LoS}=\frac{1}{1+\beta_{1}\exp[-\beta_{2}(\theta-\beta_{1})]} \tag{3}\]  
The probability of non-line-of-sight transmission is \(P_{NLoS}=1-P_{LoS}\), where \(\theta\) denotes the elevation angle from the UAV to the vehicle user and \(\beta_{1}\) and \(\beta_{2}\) are constant parameters influenced by environmental factors. The path loss between the UAV and its associated vehicle user can be expressed as  
\[\left\{ \begin{array}{l}L_{Los}=\eta_{LoS}\Big{(}\frac{4\pi f_{c}}{c}\Big{)} ^{2}d_{u,n}(l)^{2}\\ L_{NLoS}=\eta_{NLoS}\Big{(}\frac{4\pi f_{c}}{c}\Big{)}^{2}d_{u,n}(l)^{2}\end{array} \right. \tag{4}\]  
where \(\eta_{LoS}\) and \(\eta_{\text{NLoS}}\) are the attenuation factors corresponding to the line-of-sight and non-line-of-sight links, \(f_{c}\) is the carrier frequency, \(c\) denotes the speed of light, and \(d_{u,n}(l)\) denotes the distance between the UAV and the vehicle user \(v_{n}\). Therefore, we can obtain the average path loss of the UAV-to-vehicle user link as  
\[\overline{L}=P_{LoS}L_{Los}+P_{NLoS}L_{NLoS} \tag{5}\]  
The content transmission rate from the UAV to the vehicle user \(v_{n}\) at moment \(t\) can be obtained as  
\[R_{u,n}^{UV}(l)=B\cdot log_{2}\bigg{(}1+\frac{P_{U}}{\overline{L\cdot d_{u,n} (l)\cdot\sigma^{2}\cdot B}}\bigg{)} \tag{6}\]  
where \(B\) denotes the bandwidth, \(P_{U}\) denotes the transmitted power of the UAV, and \(\sigma^{2}\) denotes the Gaussian white noise variance at the receiver. The request delay for the vehicle user consists of a waiting delay \(d_{w}\) and a transmission delay \(d_{t}\) with each cache node, where the waiting time is the time the vehicle user travels without a cache node transmitting content for it before the content is fully available; the transmission delay needs to be calculated based on the transmission speed. Assuming that the length of each time slot is \(t\) and the size of the content to be transmitted is \(S_{s}\), which is an integer multiple of the content block size \(s\), and that the transmission link is broken at position \(L_{break}\), the calculation of the transmission delay is shown in Figure 4. Suppose the current time slot is the \(q\) th time slot after starting transmission, at this time, the vehicle user's position is \(l_{q}\)= \(l+t\cdot v\cdot q\), the amount of data that can be transmitted by this time slot is \(s_{t}\big{(}l_{q}\big{)}\)= \(t\cdot R\big{(}l_{q}\big{)}\), the size of the data that has not been transmitted is \(s_{r}\big{(}l_{q}\big{)}\)= \(S\sum\limits_{j=1}^{q-1}t\cdot R\big{(}l_{j}\big{)}\). If \(s_{r}\big{(}l_{q}\big{)}\)\(>s_{T}\big{(}l_{q}\big{)}\), it means that the current time slot cannot complete the content delivery and the next time slot will continue the transmission. Otherwise, the current time slot can complete content delivery; the time used for data transmission inthis time slot is \(\frac{s_{t}\left(l_{q}\right)}{R\left(l_{q}\right)}\).