  When people pick routes to minimize their travel time, the total experienced
delay, or social cost, may be significantly greater than if people followed
routes assigned to them by a social planner. This effect is accentuated when
human drivers share roads with autonomous vehicles. When routed optimally,
autonomous vehicles can make traffic networks more efficient, but when acting
selfishly, the introduction of autonomous vehicles can actually worsen
congestion. We seek to mitigate this effect by influencing routing choices via
tolling. We consider a network of parallel roads with affine latency functions
that are heterogeneous, meaning that the increase in capacity due to to the
presence of autonomous vehicles may vary from road to road. We show that if
human drivers and autonomous users have the same tolls, the social cost may be
arbitrarily worse than when optimally routed. We then prove qualities of the
optimal routing and use them to design tolls that are guaranteed to minimize
social cost at equilibrium. To the best of our knowledge, this is the first
tolling scheme that yields a unique socially optimal equilibrium for parallel
heterogeneous network with affine latency functions.
