To support rapid and accurate autonomous driving services, road environment information, which is difficult to obtain through vehicle sensors themselves, is collected and utilized through communication with surrounding infrastructure in connected vehicle networks. For this reason, we consider a scenario that utilizes infrastructure such as road side units (RSUs) and macro base station (MBS) in situations where caching of road environment information is required. Due to the rapidly changed road environment, a concept which represents a freshness of the road content, age of information (AoI), is important. Based on the AoI value, in the connected vehicle system, it is essential to keep appropriate content in the RSUs in advance, update it before the content is expired, and send the content to the vehicles which want to use it. However, too frequent content transmission for the minimum AoI leads to indiscriminate use of network resources. Furthermore, a transmission control, that content AoI and service delay are not properly considered adversely, affects user service. Therefore, it is important to find an appropriate compromise. For these reasons, the objective of this paper is about to reduce the system cost used for content delivery through the proposed system while minimizing the content AoI presented in MBS, RSUs and UVs. The transmission process, which is able to be divided into two states, i.e., content caching and service, is approached using Markov decision process (MDP) and Lyapunov optimization framework, respectively, which guarantee optimal solutions, as verified via data-intensive performance evaluation.