  Autonomous vehicles (AVs) will revolutionarize ground transport and take a
substantial role in the future transportation system. Most AVs are likely to be
electric vehicles (EVs) and they can participate in the vehicle-to-grid (V2G)
system to support various V2G services. Although it is generally infeasible for
EVs to dictate their routes, we can design AV travel plans to fulfill certain
system-wide objectives. In this paper, we focus on the AVs looking for parking
and study how they can be led to appropriate parking facilities to support V2G
services. We formulate the Coordinated Parking Problem (CPP), which can be
solved by a standard integer linear program solver but requires long
computational time. To make it more practical, we develop a distributed
algorithm to address CPP based on dual decomposition. We carry out a series of
simulations to evaluate the proposed solution methods. Our results show that
the distributed algorithm can produce nearly optimal solutions with
substantially less computational time. A coarser time scale can improve
computational time but degrade the solution quality resulting in possible
infeasible solution. Even with communication loss, the distributed algorithm
can still perform well and converge with only little degradation in speed.
