## 3 AMO Model Construction
### Agent-Based Multimode Dynamic Traffic Simulation Model
#### 3.2.1 Pre-Trip Decision Model
Time limit for reservation decisions: As per the assumptions of this study, traveler \(n\) with an original departure time \(t\) must make a reservation decision at least 30 min prior to \(t\). For instance, if a traveler has an original departure time of 07:12, they must decide whether to make a reservation by 06:42 at the latest. Determining the need for the reservation: First, assess whether the traveler's initial route passes through a reserved road. If it does not, reservation decisions are not considered. If it does, calculate the time \(t_{1}\) when the traveler would reach the entrance of the reserved road based on the initial state of travel time on that road. Then, determine if there are any remaining reservation slots available at \(t_{1}\). If available, reserve the right of passage for that time slot without adjusting the original departure time. Consequently, the reservation quota for that time slot is reduced by one. Adjusting travel time: If there are no available reservation slots at \(t_{1}\), travelers need to consider changing their departure time by leaving earlier or later. As travelers prefer to minimize the adjustment to their departure time, search for available capacity in the time slots immediately before and after \(t_{1}\). If available capacity is found, reconsider the departure time and travel mode under the reservation subsidy mechanism. After considering travel incentives, the generalized travel cost for each travel mode is as follows:  
(a) Generalized travel cost for reserved cars  
\[C_{n,\bar{I}}^{\pi_{e},car}=\eta v_{e}[t_{w}-(t+t_{t})]+(1-\eta)v_{I}[(t+t_{t}) -t_{w}]+v_{t}*t_{t}+\sum_{a}d_{a}*l-u_{re\_car} \tag{7a}\] \[t=\bar{t}\pm h*10\] (7b) \[t_{t}=\sum_{a}t_{a}\] (7c) \[u_{re\_car}=h*u_{r}\] (7d) \[P_{n}(t)=\frac{\exp\left(-\theta_{2}C_{n,\bar{I}}^{\pi_{e},car}\right)}{\sum_{l }exp\left(-\theta_{2}C_{n,\bar{I}}^{\pi_{e},car}\right)} \tag{7e}\]  
where \(C_{n,\bar{I}}^{\pi_{e},car}\) represents the generalized travel cost for traveler \(n\) choosing reserved car at time \(t\); and \(\bar{t}\) is the original departure time, assuming reservations are made in 10 min time windows. When a traveler departs \(h\) time windows earlier or later, the departure time is \(t=\bar{t}\pm h*10\). The travel time \(t_{t}\) is the shortest path time through the reserved route. \(u_{re\_car}\) is the incentive under the TRS. \(u_{r}\) is the incentive for each change of travel time window. \(P_{n}(t)\) is the probability that traveler \(n\) chooses departure time \(t\). \(\theta_{2}\) is the discrete parameter for travel time. 2. Generalized travel cost for no-reserved cars \[C^{car}_{n,k}=\eta v_{e}\big{[}t_{w}-\big{(}\overline{t}+t_{t}\big{)}\big{]}+(1- \eta)v_{l}\big{[}\big{(}\overline{t}+t_{t}\big{)}-t_{w}\big{]}+v_{t}*t_{t,k}+ \sum_{a}d_{a}*l\] (8a) \[t_{t,k}=\sum_{a}t_{k,a}\] (8b)  
Users who do not participate in the reservation system proceed with their journey according to their original departure time, denoted as \(\overline{t}\). Here, \(t_{t,k}\) represents the on-route time for path \(k\) that does not pass through any reserved roads. Non-reserved car travel does not qualify for incentive and, therefore, is not included in the incentive calculation framework. 3. Generalized travel cost for buses \[C^{bus}_{n,k}=\eta v_{e}\big{[}t_{w}-\big{(}\overline{t}+t_{t}\big{)}\big{]}+( 1-\eta)v_{l}\big{[}\big{(}\overline{t}+t_{t}\big{)}-t_{w}\big{]}+v_{t}*t_{t,k}+ f_{bus}-u_{bus}\] (9a) \[t_{t,k}=\sum_{a}t_{a,k}+t_{i}\] (9b) \[C_{n,\bar{I}}^{\pi_{e},car}=\eta v_{e}[t_{w}-(t+t_{t})]+(1-\eta)v_{I}[(t+t_{t}) -t_{w}]+v_{t}*t_{t}+\sum_{a}d_{a}*l-u_{re\_car} \tag{7a}\]0 (9c)  
For users who are unable to travel as originally planned due to a full reservation quota and need to switch to bus travel, the departure time remains unchanged at \(\overline{t}\). The on-route time for bus travel is composed of two parts: the travel time across roads, denoted as \(\sum\limits_{a}t_{a,k}\), and the waiting time for the bus, denoted as \(t_{i}\).