The IEEE 802.11p is an emerging wireless protocol dedicated for Wireless Access in the Vehicular Environment (WAVE). It employs the Enhanced Distributed Channel Access (EDCA) mechanism to access the channel. Its objective is to provide differentiated services to vehicular networks which are delay-sensitive and requires high communication throughput. In this paper, we carry out comprehensive performance analysis of the IEEE 802.11p standard. We propose a Markov chain-based analytical model that depicts accurate representation of the IEEE 802.11p MAC sub-layer. We take into account the internal collision probability that occur among different Access Categories (ACs) in the same vehicle. We also consider an unsaturated traffic condition and include the probability of finding the medium busy when sensed during the backoff period. We study the performance of the system in terms of average throughput and average time delay.