## 1 Introduction  
Traffic congestion and limited parking space are the two major problems for commuters in transportation networks. In many urban megacities, travelers may experience severe traffic congestion when completing commuting trips during morning peak hours. Since the parking space may be insufficient to meet the high parking demand in the city center, commuters may also spend much time searching for parking slots, which increases their travel costs. Under such circumstances, the critical challenge is managing traffic congestion and parking provision to reduce individual travel costs and improve social welfare. From the perspective of a transportation agency, it is essential to encourage the adoption of new travel modes or resort to new transportation management instruments. With the development of autonomous vehicle (AV) technologies, commuters may have the opportunity to purchase and utilize AVs privately in their daily lives, providing an alternative to existing travel modes. The advantages of using AVs for commuting are manifested in both individual and social (societal) aspects. From the perspective of commuters, AVs allow commuters to focus on their productive matters in vehicles with the assistance of self-driving technology. Moreover, the vehicles can self-drive to the selected parking slots without the presence of the owners. The experienced travel time cost and the cost associated with parking may be lower compared to using traditional vehicles. From the perspective of society, road traffic may be maintained in a smooth state with a certain penetration of AVs, which helps to alleviate traffic congestion and avoid traffic accidents. Traveling with AVs can also reduce vehicle emissions, especially during the congested period. Enabled by self-driving and self-parking capabilities, commuters' decision making and travel preferences may change dramatically, which may reshape the future urban travel patterns during morning peak hours. During the transition period, commuters can travel with AVs or HVs to complete morning commuting trips, which incurs a partially automated environment. Commuters traveling with different travel modes may have different behaviors toward departure time choices and parking location choices. And the departure time choices and the parking location choices of commuters interact with each other, which adds to the complexity of the problem. The network configuration also influences the parking location choices of commuters. Most relevant studies assume that the parking slots are distributed linearly along a corridor between the common workplace and the residence area, e.g., [1]. The parking slots could be grouped into on-street or off-street parking to analyze commuters' parking behaviors, e.g., [2]. In this work, we consider an ideal network for the morning commute with a single corridor and two parking clusters near the workplace. We aim to establish a modeling framework to formulate the joint decisions of commuters on departure times and parking locations in the morning commute under the partially automated environment. Furthermore, we will investigate the impacts of parking management policies and network configurations on commuters' decision making and system performance. The morning commute problem, in which a fixed number of commuters choose departure time, is formulated using a bottleneck model by [PERSON] [3]. Based on the user equilibrium (UE) principle, this classic bottleneck model has been extended to model the multidimensional decisions of commuters, such as combined departure time and route choices, e.g., [4; 5]; combined departure time and travel mode choices, e.g., [6; 7]; and the integrated morning and evening commuting patterns, e.g., [8; 9]. These studies investigate the impacts of commuters' decision making on congestion evolution or social welfare. The impacts of commuters' parking decisions on congestion evolution during the morning peak period have also been extensively analyzed by modeling the combined departure time and parking location choices.