Parking is a cumbersome part of auto travel because travelers have to search for a spot and walk from that spot to their final destination. This conventional method of parking will change with the arrival of autonomous vehicles (AV). In the near future, users of AVs get dropped off at their final destination and the occupant-free AVs search for the nearest and most convenient parking spot. Hence, individuals no longer bear the discomfort of cruising for parking while sitting in their vehicle. This paper quantifies the impact of AVs on parking occupancy and traffic flow on a corridor that connects a home zone to a downtown zone. The model considers a heterogeneous group of AVs and conventional vehicles (CV) and captures their parking behavior as they try to minimize their generalized travel costs. Insights are obtained from applying the model to two case studies with uniform and linear parking supply along the corridor. We show that (i) CVs park closer to the downtown zone in order to minimize their walking distance, whereas AVs park farther away from the downtown zone to minimize their parking search time, (ii) AVs experience a lower search time than CVs, and (iii) higher AV penetration rates reduce travel costs for both AVs and CVs.