The autonomous cars are considered as a tremendous disruptive innovation in the coming years. They enable a driving automation system to replace human drivers to control the vehicle with better recognition, decision and driving skills and ultimately enhance the road users' experience and traffic safety. They can communicate with other cars as they are ready with the Vehicle to Vehicle (V2V) communication technology based on Vehicular Ad hoc Networks (VANETs). One of the objectives of V2V communication is for the safety of all road users. Adequate reliability of routing protocol is subject of concern and must be taken into account to reach an immense standard of road safety accurately and timely. Having no reliability the critical road safety messages will be useless; consequently, the accident that might happen is unable to prevent or avoid. The purpose of this research is to investigate and analyze the quantitative measure of reliability. The reliabilities of a reactive single-path AODV and a multipath AOMDV routing protocols that comply with road safety requirements in various traffic conditions are studied. The traffic conditions that may impact the internetworking of autonomous cars include node density, size of road area and speed of the nodes. The methods used in this study are based on simulations by using Network Simulator version-2 (NS2) as a network simulator and Simulation of Urban Mobility (SUMO) as a mobility simulator. The simulation results show that both routing protocols, a single-path AODV and a multi-path AOMDV, satisfy the road safety requirements in some conditions. AODV is better in packet delivery, whereas AOMDV has a better performance on average end to end delay. This study is expected to contribute to the determination of the appropriate protocol for use in road safety applications under certain traffic conditions. In conclusion, the reliability of routing protocol is an essential factor to consider in the operation of VANET-based autonomous cars so that the safety and comfort of road users can be guaranteed.