## 2 Model Formulation  
### Model Setting  
Consider a single corridor connecting a residential area and a workplace (central business district, CBD), as shown in Figure 1. A bottleneck exists at the exit of this corridor so commuters may experience queuing time to traverse the congestion segment. Following [PERSON] et al. (2018), we assume the parking slots around the workplace can be categorized into two discrete clusters according to the distance between each cluster and the workplace. Specifically, the central cluster represents a group of parking slots close to the workplace. And the peripheral cluster includes parking slots located relatively far from the workplace. Let \(j\) denote the index of the parking cluster where \(j=1\) represents the central cluster and \(j=2\) represents the peripheral cluster. In practice, there is a sufficient number of parking slots in the peripheral area, whereas the parking space near the CBD is usually limited. Let \(K_{j}\) denote the parking capacity, i.e., the number of parking slots in each cluster. \(K_{2}\) should be large enough to accommodate all commuters, but \(K_{1}\) may not meet the parking demand in the CBD area. In other words, we assume a limited capacity for the central cluster. During the morning peak period, there are \(N\) commuters travelling from the residential area to the workplace in the CBD. A commuter may travel by an autonomous vehicle (AV) or a human-driven vehicle (HV). Let \(N^{a}\) and \(N^{h}\) denote the travel demand for AVs and HVs, respectively. The two groups of commuters follow different procedures to complete their morning commuting trips. As illustrated in Figure 2, the HV commuters will travel from home to a selected parking location within a cluster and then walk back from the parking location to the workplace. Unlike HV commuters, AV commuters can drop off directly at the workplace, and their vehicles will self-drive to the parking slots. The differences in the travel process result in different cost considerations between the two groups of commuters. The commuters decide on departure time from home (\(t\)) and the parking location choices (\(j\)). When the departure rate from home exceeds the bottleneck capacity \(s\), a queue  
Figure 1: A single-corridor network with two parking clusters. Figure 2: The departure and parking sequence of HV and AV commuters. forms, and commuters experience a certain level of queuing time to pass the congested corridor. The travel time experienced by commuters departing at time \(t\) is composed of free-flow travel time and queuing time. Without loss of generality, the free-flow travel time on this corridor is assumed to be \(0\). Let \(Q(t)\) denote the queuing length, i.e., the total number of vehicles waiting at the bottleneck at time \(t\). Thus, the travel time is given by \(T(t)=\frac{Q(t)}{s}\). Next, we proceed to define the individual travel costs for both AV and HV commuters. Each commuter experiences a bottleneck cost, including travel time cost and schedule delay cost, as in [PERSON]'s bottleneck model. We assume that the AV and HV commuters are heterogeneous regarding the value of time. Let \(\alpha^{a}\) and \(\alpha^{h}\) denote the values of time for AV commuters and HV commuters, respectively. The commuters only experience schedule delay costs for early arrivals, as late arrivals are not allowed. Based on the travel process discussed earlier, the schedule delay time is \(t^{*}-t-T(t)\) for AV commuters and \(t^{*}-t-T(t)-w_{j}\) for HV commuters. In addition to bottleneck cost, the topology of the single-corridor network affects the individual travel costs of two groups of commuters. As illustrated in Figure 1, the closer cluster corresponds to a lower travel distance between the parking location and the workplace. In contrast, the travel distance between the parking location and the workplace will increase if commuters park at the farther cluster.