The advent of autonomous vehicles (AVs) with self-parking capability puts forward new requirements for parking policy and management. In a transportation system with both general and dedicated AV lanes, this work aims to examine and compare the effectiveness of different parking policies on the morning commute. To be specific, three policies of parking space allocation, namely, first-come-first-service (FCFS), advanced reservation (AR), and their combination (CB), are proposed to guide the commuters’ travel choices. Commuters can drive regular vehicles (RVs) alone on the general lane or ridesharing shared autonomous vehicles (SAVs) on the dedicated AV lane. The occurrence conditions and the resultant SAV penetration rates for various scenarios under three parking policies are revealed. The area division for various scenarios with respect to two key parameters is presented, and the typical departure patterns are plotted as well. The numerical results clarify that the CB policy always has a better effect on the total travel cost than FCFS and AR policies. The optimal CB policy is quantified in terms of the optimal amount of all parking spaces and the proportion of unreserved parking spaces. These findings help to improve the spatial and temporal distribution of traffic flow and allocate transportation resources efficiently in the coming era of autonomous driving.