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The development of vehicular communication technology can make more intelligent transportation systems (ITSs) by enabling a large number of potential applications. In particular, infrastructure-to-vehicle (I2V) communication will support ITS applications and provide inexpensive high-rate Internet access as well. Thus, a study on I2V communications may improve the quality of experience of end users in vehicles, such as drivers and passengers. To this end, we propose a medium access control (MAC) protocol for I2V communications to improve the fairness of node throughput while maximizing the expected system throughput. We derive the way of estimating road traffic to precisely control the transmission probability of vehicles for maximizing system throughput. The estimation is performed by utilizing the spacing distribution model in transportation systems. Furthermore, we present a threshold to limit the number of transmitted packets for the fairness of the vehicles. The threshold is set based on the achievable node throughput and the estimated sojourn time. Through extensive simulations based on the empirical vehicular trajectory data, we demonstrate the improved performance of the proposed MAC protocol. The test results show that the expected system throughput is increased by more than 21.3% and that Jain's fairness index with regard to the number of transmitted packets among the nodes is close to 1.