## 2 System Model  
In this section, as shown in Figure 1, we consider a bidirectional two-lane urban area which has \(2I\) lanes that have the same size with length \(E\) and width \(D\). \(i\) and \(i+I,i\in[1,I]\) denote the two lanes of the dual carriageway, respectively. The traffic flow is different in different lanes, and we assume the vehicle number of an area of lane \(i\) follows a Poisson Point Process, with a rate of \(\lambda_{i}\) per unit area [22]. For example, \(K\) denotes the vehicle number of lane \(i\) and the probability distribution function of \(K\):  
\[P_{i}\{K=k\}=\frac{\left(\lambda_{i}DE\right)^{k}}{k!}e^{-\lambda_{i}DE} \tag{1}\]Especially, the two lanes of a dual carriageway have the same distribution parameter, and there holds \(\lambda_{i}=\lambda_{i+1},i\in[1,I]\). Assuming that the speed of vehicles on different streets is different, and the speed of vehicles in the same lanes follows the same Truncated Normal Distribution [23], the probability density function of speed, defined by \(s_{i}\) of vehicles on lane \(i\), is given as follows:  
\[f(s_{i})=\left\{ \begin{array}{ccc}\frac{c_{i}}{\sqrt{2\pi\sigma_{i}}}e^{- \frac{(y_{i}-y_{i})^{2}}{2\sigma_{i}^{2}}}&s_{\min}\leq s_{i}\leq s_{\max}\\ 0&,\ \ \ else\end{array} \right. \tag{2}\]  
where \(\mu_{i}\) and \(\sigma_{i}\) denote the mean and standard deviation of \(s_{i}\), and parameter \(c_{i}\) ensures the accumulated probability of \(f(s_{i})\) equals 1 in the range \([s_{\min},s_{\max}]\), which can be used to determine the value of \(c_{i}\), especially, \(s_{i}\) and \(s_{i+1}\) have the same probability density function. Because the speed of any two vehicles is independent of each other, the joint probability density function of speed \(s_{i}^{x}\) and speed \(s_{i}^{y}\) of two vehicles in lane \(i\) is derived as follows:  
\[ \begin{array}{rl}f(s_{i}^{x},s_{i}^{y})&=f(s_{i}^{x})\cdot f(s_{i}^{y})\\ &=\left\{\begin{array}{ccc}\frac{c_{i}^{2}}{2\pi\sigma_{i}^{2}}e^{-\frac{(y _{i}^{x}-y_{i})^{2}+(y_{i}^{y}-y_{i})^{2}}{2\sigma_{i}^{2}}}&s_{\min}\leq s_{i} ^{x}\leq s_{\max},s_{\min}\leq s_{i}^{y}\leq s_{\max}\\ 0&,\ \ \ \ \ \ \ \ \ \ \ else\end{array}\right.\end{array}  \tag{3}\]  
The distribution function of speed \(s_{i}\) can be derived from Formula (2) as follows:  
\[F(s_{i})=\left\{ \begin{array}{ccc}1&,&s_{i}>s_{\max}\\ \int_{s_{\min}}^{s_{i}}f(t)dt&,&s_{\min}\leq s_{i}\leq s_{\max}\\ 0&,&s_{i}<s_{\min}\end{array} \right. \tag{4}\]  
Each intersection in our system has an RSU. RSUs connect with the internet, and RSUs are linked to their neighboring counterparts, whereby vehicles can obtain all desired content. Assuming that \(M\) RSUs exist in this area, RSU is denoted by \(R_{m}\), and the subscript \(m\) denotes the sequence number of \(R_{m}\), all RSUs have the same communication range with \(R^{rsu}\), as well as the same maximum transmission rate with \(R^{max}\), and the number of  
Figure 1: System model. request arrival at \(R_{m},m\in[1,M]\) obeys the distribution of Poisson Process with parameter \(\lambda_{m}^{rstu}\). Vehicles in our system are denoted by \(V_{x}\), where the subscript \(x\) denotes the sequence number of \(V_{x}\), and all vehicles have the same transmission range with \(r^{v}\). The authors of [24] indicated that the request for content approximately follows a Zipf distribution. Accordingly, we assume that the amount of content in the content library is \(L\), and every content has the same size of \(W\). Vehicles' requests for content in the library obeys the Zipf distribution, and content with higher popularity has a higher probability of being requested. The probability of requesting the content with popularity ranked at \(\tau\) is given as follows:  
\[f_{\tau}=\frac{\tau^{-\gamma}}{\sum\limits_{j=1}^{L}j^{-\gamma}},\tau\in[1,L] \tag{5}\]  
where \(\gamma\) means the parameter of Zipf distribution. As the value of \(\gamma\) increases, the vehicles will more frequently request content with high popularity. \(\tau\) denotes the popularity rank of content in the library.