Abstract. Reliable and efficient data broadcasting is essential in vehicular networks to provide safety-critical and commercial service messages on the road. There is still no comprehensive analysis of IEEE 802.11p based MAC that portrays the presence of buffer memory in vehicular networks. Besides, most of the analytical works do not fulfill some of the IEEE 802.11p specifications, such as short retry limit and back-off timer freezing. This paper proposes a 1-D and 2-D Markov model to analyze mathematically IEEE 802.11p based MAC for safety and non-safety messages respectively. The work presented in this paper takes into account the traffic arrival along with the first-order buffer memory and freezing of the back-off timer as well, to utilize the channel efficiently and provide higher accuracy in estimation of channel access, yielding more precise results of the system throughput for non-safety messages and lower delay for safety messages. Furthermore, back-off stages with a short retry limit were applied for non-safety messages in order to meet the IEEE 802.11p specifications, guaranteeing that no packet is served indefinitely, avoiding the overestimation of system throughput. A simulation was carried out to validate the analytical results of our model.