In vehicular networks, the safety-related messages (emergency and periodic messages) and non-safety message (RFS: request for service message) should share the scarce wireless resource. Emergency messages deliver time-critical information with guaranteed reliability, e.g.road-safety information, whereas periodic ones convey normal status update information, e.g.vehicular positions, show that is less time- and loss-critical. The RFS message is used for reserving Internet data service through the infrastructure on the road. In the channel access for vehicles, the synchronization interval (SI) is repeated every 100 ms and each SI is divided by one control channel interval (CCHI) for the transmission of safety-related messages and RFS message and by one service channel interval (SCHI) for the Internet service from the roadside infrastructure. It is crucial to set the length of CCHI appropriately in the SI because of the dynamic environment of VANETs. In this paper, we consider two optimization problems of message transmissions depending on whether the length of CCHI is flexible or not: 1) a fixed CCHI (non-adaptive) and 2) a variable CCHI (adaptive), respectively, and obtain the optimal MAC parameters where we adopt the IEEE 802.11e enhanced distributed channel access (EDCA) protocol with a "strict'' priority for the emergency message. Finally, we conduct extensive simulations to validate our analytical findings.