Quality of service (QoS) and queue management are critical issues for the broadcast scheme of IEEE 802.11p systems in vehicular ad hoc networks (VANETs). However, existing 1- dimensional (1-D) Markov chain models of 802.11p systems are unable to capture the complete QoS performance and queuing behavior due to the lack of an adequate finite buffer model. We present a 2-dimensional (2-D) Markov chain that integrates the broadcast scheme of the 802.11p system and the queuing process into one model. The extra dimension, which models the queue length, allows us to accurately capture the important QoS measures, delay and loss, plus throughput and queue length, for realistic 802.11p systems with finite buffer under finite load. We derive a simplified method to solve the steady state probabilities of the 2-D Markov chain. Our 2-D Markov chain model is the first finite buffer model defined and solved for the broadcast scheme of 802.11p systems. The 2-D model solutions are validated by extensive simulations. Our analyses reveal that the lack of binary exponential backoff and retransmission in the 802.11p system results in poor QoS performance during heavy traffic load, particularly for large VANETs. We demonstrate that our model provides traffic control guidelines to maintain good QoS performance for VANETs.