## 3 Network Scenario and Problem Statement  
We investigate a vehicular scenario including static roadside units with the provision of internet access, and mobile vehicular nodes equipped with devices offering V2V and V2U communication capabilities (e.g., IEEE 802.11p). A content request and acquisition process starts with a vehicular node sending out a content query to a meeting roadside unit. The roadside unit gathers the queries during a segment of time, named a storage cycle and denoted by \(\tau\), and then passes these queries to an online control center. The control center determines a data distribution solution based on a comprehensive analysis of the queries from vehicular nodes, the storage of roadside units and the vehicle routing plans. After the contents are distributed to those roadside units which may encounter the request senders in the next storage cycle \(\tau+1\), the requests could be satisfied by the units via V2U communications. Note that, in our scheme, the data distribution is executed at the beginning of a storage cycle, and then the contents will be carried by relevant roadside units during the whole cycle. When the next storage cycle starts, the new distribution determines whether the already existing contents should be deleted or not. For example, at the start of \(\tau+1\), for content carried by a roadside unit in \(\tau\), if it is not allocated to this unit currently, it is erased from the storage spaces; otherwise, it remains there during \(\tau+1\). Although the network updating after a storage cycle takes some time, it may be short and acceptable for three reasons. First, the data distribution solution is calculated by the control center with a high computing and communication capability, rather than the resource-restricted vehicular nodes and roadside units. Additionally, the updating time of a roadside unit is only used for data receiving from the control center. In other words, except this time, the roadside units are always serving for vehicular nodes' data queries. Moreover, dividing a large scenario into several small areas as well as a relatively short storage cycle is helpful to reduce the amount of data and hence shorten the updating time. For a clear presentation, the primary symbols that will be used throughout this article are listed in Table 1 with some comments below. In the content request matrix \(F\), if a vehicular node \(v_{i}\) requests content \(c_{k}\) in \(\tau\), then \(f_{ik}=1\); otherwise, \(f_{ik}=0\). In the encountering matrix \(G\), if a vehicular node \(v_{i}\) will encounter a roadside unit \(u_{j}\) in \(\tau+1\) according to its routing plan, then \(g_{ij}=1\); otherwise, \(g_{ij}=0\). In addition, in the encountering latency matrix \(H\), if a roadside unit \(u_{j}\) is the \(x\)th one which will be met by a vehicular node \(v_{i}\) in \(\tau+1\), then \(h_{ij}=x\) (\(0<x\leq|\mathcal{U}|\)); otherwise, \(h_{ij}=0\). Content \(\mathcal{C}\) is originally hosted on a server connected with the internet, which can be downloaded through the broadband access at \(\mathcal{U}\). We assume the valid duration of a data query equals \(\tau\); each content has the same size \(s\); the storage capacity of a roadside unit is an integer multiple of \(s\). The storage space for a content is known as a storage cell, so the number of storage cells in a roadside unit is an integer, i.e., \(w(j)\in\mathbb{N}^{+}\). From the content request and acquisition process, it is observed that the data replication at roadside units affects the number of satisfied requests and hence the access ratio, and influences the access delay considering the waiting time for encounters between vehicular nodes and roadside units. Taking the maximum access ratio as an objective, the problem of data distribution to roadside units is similar to a 0-1 knapsack problem with the number of satisfied requests as the value and the size of content as the weight.