It is known that autonomous vehicles are capable of maintaining shorter headways and distances when they form platoons of vehicles. Thus, deployment of autonomous vehicles can result in roadway flow capacity increases in traffic networks. Consequently, it is envisioned that their deployment will boost the overall capacity of the network. In this paper, we consider a nonatomic routing game on a traffic network with inelastic (fixed) demands for the set of network O/D pairs, and study how replacing a fraction of regular (i.e. nonautonomous) vehicles by autonomous vehicles will affect the network total delay, under the assumption that the vehicles choose their routes selfishly. Using well known US bureau of public roads (BPR) traffic delay models, we show that the resulting Wardrop equilibrium is not necessarily unique even in its weak sense for networks with mixed autonomy. We derive the conditions under which the total network delay is guaranteed to not increase as a result of increasing the ratio of autonomous vehicles. However, we also show that when these conditions do not hold, counter intuitive behaviors might occur: the total delay can grow by increasing the fraction of autonomous vehicles in the network. In particular, we prove that for networks with a single O/D pair, if the road degree of capacity asymmetry (i.e. the ratio between the road capacity when all vehicles are regular and the road capacity when all vehicles are autonomous) is homogeneous, the total network delay is 1) unique, and 2) a nonincreasing continuous function of network autonomy fraction. We show that for heterogeneous degrees of capacity asymmetry, the total delay is not unique, and it can further grow when the fraction of autonomous vehicles increases. We demonstrate that similar behaviors may be observed in networks with multiple O/D pairs.