# Hybrid Cooperative Cache Based on Temporal Convolutional Networks in Vehicular Edge Network
## 3 System Model
### Problem Formulation  
As shown in Figure 1, it is assumed that \(M\) RSU servers are deployed in a cooperation area, where the set of RSU servers is \(R=\{r_{1},r_{2},\ldots,r_{M}\}\), the cache capacity is \(U=\{u_{1},u_{2},\ldots,u_{M}\}\), and the set of intelligent vehicles is \(N\). Let \(r_{0}\) denote a central server and \(c_{0}\) represent its capacity. By default, the storage capacity of the central server is unlimited. Assume that the central server has \(F\) content sets of \(E=\{e_{1},e_{2},\ldots,e_{F}\}\), and the corresponding size of each content is \(S=\{s_{1},s_{2},\ldots,s_{F}\}\). Each user individually requests content \(e_{i}(1\leq i\leq F)\) from RSUs in the cooperation area. We use \(P_{m,i,t}\) to express the popularity of the content \(e_{i}\) on RSU \(r_{m}\) at time \(t\). We assume that content popularity is static during a given time interval. Cached information can be shared among collaborating RSU. We constructed a content cache matrix \(X=(x_{m,i})_{M\times F}\). \[x_{m,i}= \begin{cases}1&\text{if content $e_{i}$ is cached on $r_{m}$}\\ 0&\text{otherwise}\end{cases}  \tag{1}\]  
The user's request mode for content will not change during the time slot \(\triangle t\). Based on this, we designed a cooperative caching strategy to maximize user-perceived QoE. Since content delivery delays are the most critical factor affecting QoE, we chose it as the main indicator of system evaluation. According to the network model of this paper, the content delivery delay is divided into three parts: the content transmission delay from the central server to the RSU, the content sharing delay between the RSU, and the content acquisition delay from the local RSU to the vehicle. We consider that the communication between vehicles and nodes uses the dedicated short-range communication technology based on 802.11 p and the communication between RSU uses wired links. In short, the problem of edge caching translates into how to minimize the overall latency under the constraint of cache capacity. According to [PERSON]'s theorem, the transmission rate between cooperative vehicles and RSU in the cluster is calculated as:  
\[d_{r,n}=B\log_{2}\biggl{(}1+\frac{Ph_{n}(\tau(x,V_{n}))}{\sigma^{2}}\biggr{)} \tag{2}\]  
where \(B\) is the transmission bandwidth, \(P\) is the transmission power, \(\sigma^{2}\) is Gaussian white noise, \(h_{n}(\tau(x,V_{n}))\) is the channel gain modeling of vehicle \(n\)[29], \(x\) represents vehicles, RSU, and central servers. The transmission delay from RSU \(r_{n}\) to RSU \(r_{m}\) consists of two parts: (1) transmission delay \(d^{t}_{r_{n},r_{m}}\) ; (2) propagation delay \(d^{p}_{r_{n},r_{m}}\). Therefore, the transmission delay \(d_{r_{n},r_{m},i}\) for content \(e_{i}\) from RSU \(r_{n}\) to RSU \(r_{m}\) is as follows:  
\[d_{r_{n},r_{m},i}=d^{t}_{r_{n},r_{m}}s_{i}+d^{p}_{r_{n},r_{m}} \tag{3}\]  
When sending content \(e_{i}\) to \(r_{m}\), the cooperation RSU with the smallest delivery delay is:  
\[r_{\varphi}=\operatorname*{arg\,min}_{r_{n}}\{d_{r_{n},r_{m},i}\mid\forall r_{ n}\in\{R\cup\{r_{0}\}\},x_{n,i}=1\} \tag{4}\]  
The content delivery delay of the RSU \(r_{m}\) acquiring content \(e_{i}\) is \(d_{r_{\varphi}r_{m},i}\). If the content \(e_{i}\) is cached locally on the RSU server \(r_{m}\), \(r_{\varphi}=r_{m}\), the content delivery delay is \(d_{r_{\varphi},r_{m},i}=0\); if the content \(e_{i}\) is not cached on \(r_{m}\), but on the rest of the RSU within the collaboration scope, the collaborative RSU transmission content with the minimum delivery delay will be selected. In this case, \(r_{\varphi}\in R\), the content delivery of the acquisition request is delayed to \(d_{r_{\varphi}r_{m},i}\); if the content \(e_{i}\) is not cached in any RSU server within the scope of collaboration, but is transferred from the central server to the local RSU and distributed to the user, then \(r_{\varphi}\
otin R\), the content delivery of the get request is delayed to \(d_{r_{\varphi}r_{m},i}\).