  We consider the problem of a single Autonomous Vehicle (AV) merging into
traffic consisting only of Human Driven Vehicles (HDVs) with the goal of
minimizing both the travel time and energy consumption of the entire group of
vehicles involved in the merging process. This is done by controlling only the
AV and determining both the optimal merging sequence and the optimal AV
trajectory associated with it. We derive an optimal index policy which
prescribes the merging position of the AV within the group of HDVs. We also
specify conditions under which the optimal index corresponds to the AV merging
before all HDVs or after all HDVs, in which case no interaction of the AV with
the HDVs is required. Simulation results are included to validate the optimal
index policy and demonstrate cases where optimal merging can be achieved
without requiring any explicit assumptions regarding human driving behavior.
