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This paper proposes a scheduling algorithm for non-real-time traffic in Vehicle to Infrastructure (V2I) networks. The scheduler operates at the link layer and uses the contention-free, poll-based access mode of the 802.11e standard. Our proposal exploits two specific features of V2I that are not present in other wireless systems. First, the fact that vehicles are constrained to a predefined area (the road segment under radio coverage) which can be characterized in terms of packet error ratio (PER). Second, that it is possible to know the vehicle speed, either accurately or approximately. These characteristics allow us to model the data transmission process in V2I as a dynamical system. However, the unpredictable arrivals of new vehicles make it difficult to directly apply dynamic programming to obtain the optimum scheduler. We overcome this limitation by developing a tractable formulation of the problem, similar to a classical linear quadratic regulator design problem but with the significant difference that constraints are included. We propose a novel algorithmic solution that can be efficiently computed and can easily incorporate quality of service differentiation. The scheduler is compared to three other feasible schemes, assessing the impact of the system parameters in the performance. Numerical results show that the proposed scheme is more beneficial when the average PER values have notable variations along the covered area.