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This paper studies a trajectory-based traffic management (TTM) problem for the purpose of managing traffic in a road facility reserved exclusively for autonomous vehicles (AV). The base TTM model aims to find optimal trajectories for multiple AVs while resolving inter-vehicle conflicts in the most generic way. The model is formulated as a mixed integer program (MIP) that can be solved using off-the-shelf solvers. To improve computational efficiency, a specialized algorithm based on the rolling horizon approach is also developed. We then show that the base TTM model can be easily extended to first accommodate scheduling decisions (the TTMS model) and to further impose equity constraints (the TTMSE model). For the simplest network and homogeneous users, solutions to TTMS and TTMSE are similar, respectively, to system optimal (SO) and user equilibrium (UE) solutions of Vickrey’s bottleneck model …