## 7 Conclusions  
This paper investigates the decision making of commuters and the impacts of parking management policies on the morning commute problem under a partially automated environment. We consider a single-corridor network with two discrete parking clusters near the workplace. The commuters make joint decisions on departure time choices and parking location choices for completing the trip from home to work. To formulate the joint decisions of commuters, we extend [PERSON]'s bottleneck model by incorporating the influences of parking locations and the travel modes used by travelers. We derive the equilibrium conditions to solve the dynamic user equilibrium problem. The equilibrium state is obtained when no commuters can further reduce their travel costs by unilaterally altering departure times or parking location choices. Moreover, we examine the impacts of parking fees and parking capacity provision on system performance to provide parking management implications. Considering that parking slots located in the central area and the peripheral area are offered, we examine the parking preferences of AV commuters and HV commuters for commuting trips separately. Considering that commuters make parking location choices to minimize their travel costs, we analyze the parking preferences by comparing the individual travel costs of a commuter between choosing two different parking clusters. We find that the parking preferences of commuters depend on the range of the difference in parking prices and the travel time between the workplace and parking location. Specifically, our analytical results reveal that all commuters prefer the central cluster when the difference in parking fees between the two clusters is low. When the difference in parking fees is very high, all commuters prefer the peripheral cluster in order to reduce their travel costs. Otherwise, the parking preferences of commuters are characterized by both the range of differences in parking prices and the relation between the self driving time of AV commuters and the walking time of HV commuters for commuting between the workplace and the parking cluster. Furthermore, we investigate the impacts of the parking fee and the parking capacity of the central cluster on the total travel cost. With insufficient parking capacity at the central cluster, the total travel cost will decrease if we offer more parking slots at this cluster. This finding implies that we can attract more commuters to parking at the central cluster if we can offer more parking slots to the commuters who prefer this cluster. As for the effects of parking fees, we find that the total travel cost increases with the parking price at the central cluster, whereas it decreases with the parking price at the peripheral cluster. Thus, it is possible to improve system performance by lowering the parking price at the central cluster when needed. Based on the aforementioned equilibrium analysis, we investigate the optimal design of the parking price at the central cluster in order to minimize the total travel cost. The results regarding the parking capacity and the parking fee of the central cluster provide managerial insights to the public parking manager in order to better regulate the parking market for the morning commute. In future research, we may extend this work in the following directions. First, we may consider more realistic parking location scenarios and investigate the optimal parking provision schemes. Second, the long-term impacts of the introduction of autonomous vehicles should be incorporated by formulating the mode choice of commuters. Formal analysis, Z.L. ; methodology, Z.L. and Y.L. ; writing--original draft, Z.L. ; supervision, J.W. ; funding acquisition, Y.L. ; conceptualization, Z.L. and Y.L. ; validation, J.W. ; writing--review and editing, Y.L. and J.W. All authors have read and agreed to the published version of the manuscript.