Vehicular ad-hoc network (VANET) uses 'mobile internet' to facilitate the communication between vehicles and with the goal to ensure road safety and achieve secure communication. Thus the reliability of this type of networks is of paramount significance. The safety-related messages are disseminated in VANETs, on the wireless medium through vehicle to vehicle (V2V) and Vehicle to roadside (V2R) communications. Hence, the Reliability of network is an essential requirement. This paper considers the effect of vehicle transmission range and vehicle density on the connectivity probability. In addition, a reliability model which takes into account minimal safe headwayamong nearby vehicles at highway tunnel is specified. The reason is that under the tunnel Global Positioning System (GPS), a component of onboard unit (OBU) needs a rich line of sight for perfect services, because due to signal interference, the GPS does not work properly. Though, in the case of a fully connected network, there are chances of danger between vehicles which are close to each other. Therefore, the network is not safe, as accidents and collision can happen at any time. Hence, maintaining the minimal safe headway distance under the tunnel is interesting and useful for VANET. The obtained results show that the little difference of the minimal safe headway under the tunnel can cause a serious change in the entire network reliability. Suggesting that while designing the network reliability models the safe headway cannot be ignored.