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Traditional studies focused on the transmission capacity of vehicular ad hoc network (VANET) contains two deficiencies: the lack of a realistic model mimicking the behaviors of vehicles and the failure to consider the impacts from enhanced distributed channel access (EDCA) mechanisms applied by IEEE 802.11p. In this paper, the car-following model is introduced to describe the distribution of vehicles, and an EDCA-based linear VANET model is analyzed. Compared to previous works, a tighter transmission capacity upper bound in a large-scale fading environment is calculated. Furthermore, under Rayleigh fading channels, an elementary expression of transmission capacity fitting a sparse vehicles scenario and an upper bound of transmission capacity applicable to a dense scenario are obtained. In conclusion, the transmission capacity of a linear VANET is illustrated by the elementary expression in a sparse vehicles scenario and the upper bound in a dense vehicles scenario. The simulation results are well constrained by the proposed theoretical expression and upper bound.