As the channel conditions experienced by vehicular users in cellular networks vary as they move, we investigate to what extent the quality of channel allocation could be improved by exploiting predictions on future data rates in non-stationary environments. Assuming mean future rates can be computed from Signal-to-Noise Ratio (SNR) maps, we propose an algorithm which predicts future throughputs over a short-term horizon at regular time intervals, and then uses this extra-knowledge for improved online channel allocation. The prediction of future throughputs is obtained by solving a relaxed version of the problem using a projected gradient algorithm. When the transmit powers of the base stations can be varied over time, a straightforward extension of our algorithm can be used for the joint optimization of channel allocation and transmit power control under average and maximum power constraints. Using event-driven simulations, we compare the performance of the proposed algorithms against those of other channel allocation algorithms, including the Proportional Fair (PF) scheduler, which is known to be optimal in stationary environments, and the (PF)$^2$S scheduler, which was devised for mobiles nodes in non-stationary environments. The simulated scenarios, which cover the cases with and without power control, include scenarios with multiple base stations and are based on realistic mobility traces generated using the road traffic simulator SUMO. Simulation results show that the proposed algorithms outperform the other algorithms and that exploiting the knowledge of future radio conditions allows a significantly better channel allocation.