## 4 Problem Formulation  
### Block Access Cost  
Considering the process in which a vehicle requests access to a block from an RSU within the cluster, we define the decision variable \(x_{ik}\), which determines the storage status of a block in an RSU. This variable indicates whether block \(b_{k}\) is stored in RSU \(r_{i}\). The decision variable set for RSU cluster \(C_{l}\) is denoted as \(X_{l}=\{x_{ik}|r_{i}\in C_{l},b_{k}\in B\}\) which forms an \(N_{l}\times K\) matrix. Here, \(x_{ik}=1\) indicates that RSU \(r_{i}\) has stored block \(b_{k}\), while \(x_{ik}=0\) indicates that RSU \(r_{i}\) does not store block \(b_{k}\). The block allocation decision table \(X\) is maintained by the cloud server and synchronized across all RSUs in the cluster. Additionally, each RSU can update this table based on local real-time network conditions. If a vehicle requests block \(b_{k}\) data from RSU \(r_{i}\) while \(x_{ik}=0\) (i.e., RSU \(r_{i}\) does not store the block \(b_{k}\) data), the RSU must query \(X_{l}\) to identify the RSU within the cluster that holds the complete copy of block \(b_{k}\) and has the lowest expected access latency. Let RSU \(r_{j}\) be the selected node that retrieves the block and transmits it to RSU \(r_{i}\), which then forwards the block to the requesting vehicle. Thus, the latency cost for vehicle \(v_{m}\) to obtain block \(b_{k}\) from RSU \(r_{i}\) is defined as follows:  
\[TD_{mk}=TD(r_{i},v_{m},b_{k})+(1-x_{ik})\cdot TD(r_{j},r_{i},b_{k}) \tag{8}\]Assuming that the service ranges of RSUs in the system do not overlap, an RSU can transmit block data to a vehicle only when the vehicle is within its coverage area. If the retrieval delay for block data from an RSU exceeds the vehicle's dwell time within the RSU's coverage, the vehicle must instead obtain the data from a remote cloud server via a backhaul link, discarding any incomplete data fragments [24]. This process incurs a higher additional access latency cost. We define the set of blocks of interest for vehicle \(v_{m}\) as \(B_{m}=\{b_{k}|b_{k}\in B,P_{mk}>0\,\}\). Let \(\Delta C\) denote the cost of a single data access from the cloud server. For a vehicle \(v_{m}\) located within the coverage area of RSU \(r_{i}\), we define the vehicle's dwell time within vehicle \(v_{m}\)'s coverage as \(t_{m}^{d}\). Given the block set \(B_{m}\), the total block access cost for vehicle \(v_{m}\) is defined as follows:  
\[C_{m}=\left\{\begin{array}{cc}\sum\limits_{b_{k}\in B_{m}}TD_{mk}\cdot P_{mk},&\sum\limits_{b_{k}\in B_{m}}TD_{mk}\leq t_{m}^{d}\\ \Delta C+\sum\limits_{b_{k}\in B_{m}}TD_{mk}\cdot P_{mk},&\sum\limits_{b_{k} \in B_{m}}TD_{mk}>t_{m}^{d}\end{array}\right. \tag{9}\]  
For the overall vehicle access process, the access cost is determined by the following factors:  
1. The vehicle's access probability for a block.
2. The latency cost for the vehicle to retrieve the block from an RSU.
3. Whether the vehicle can obtain all required block data directly from RSUs.  
Among these factors, the latency cost for a vehicle to retrieve a block from an RSU is influenced by both the clustering strategy and the block allocation strategy within the cluster. This latency cost directly impacts whether the vehicle needs to retrieve data via the backhaul link from the remote cloud server. Therefore, it is essential to design an effective collaborative storage scheme for RSU clusters to optimize the access cost for vehicles served by the cluster.