  We study routing behavior in transportation networks with mixed autonomy,
that is, networks in which a fraction of the vehicles on each road are equipped
with autonomous capabilities such as adaptive cruise control that enable
reduced headways and increased road capacity. Motivated by capacity models
developed for such roads with mixed autonomy, we consider transportation
networks in which the delay on each road or link is an affine function of two
quantities: the number of vehicles with autonomous capabilities on the link and
the number of regular vehicles on the link. We particularly study the price of
anarchy for such networks, that is, the ratio of the total delay experienced by
selfish routing to the socially optimal routing policy. Unlike the case when
all vehicles are of the same type, for which the price of anarchy is known to
be bounded, we first show that the price of anarchy can be arbitrarily large
for such mixed autonomous networks. Next, we define a notion of asymmetry equal
to the maximum possible travel time improvement due to the presence of
autonomous vehicles. We show that when the degree of asymmetry of all links in
the network is bounded by a factor less than 4, the price of anarchy is
bounded. We also bound the bicriteria, which is a bound on the cost of
selfishly routing traffic compared to the cost of optimally routing additional
traffic. These bounds depend on the degree of asymmetry and recover classical
bounds on the price of anarchy and bicriteria in the case when no asymmetry
exists. Further, we show with examples that these bound are tight in particular
cases.
