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Recent developments in vehicular traffic have brought about the concept of lane-free traffic, challenging the traditional notion of parallel lanes, allowing vehicles to potentially drive at any arbitrary lateral location of the road. In this paper, we investigate the potential lines strategy proposed in our previous study for an efficient lateral distribution of vehicles in automated lane-free freeways. Potential lines allow for structured lane-free traffic where each vehicle receives a desired lateral location based on its desired speed. To this end, we mimic the behavior of conventional driving by assigning the right side of the road to slower vehicles while faster vehicles are led toward the left. As a result, the road surface effectively forms a speed-based hierarchy, with vehicles flowing smoothly from right to left in a monotonic increase of speed. We utilize the Probability Integral Transform approach to have a uniform lateral distribution …