## 3 Methodology  
### Research Framework  
The main objective of this paper is to create a DRT model, in which the feeder bus route, starting at the bus depots and ending at the rail station, are designed to assign vehicles to cover all pickup locations to transport passengers to the rail station. Passengers place some travel orders by using a cell phone app that involves pickup or drop off locations, the boarding time window, and the predetermined subway schedule. The open GIS tool is used to calculate the real traffic distances and times between bus depots, demand points, and rail stations in the study area. During the process of designing the DRT model, a mixed-integer programming model is presented to reveal the optimal relationship of design efficiency between the feeder bus routing and the schedule considering the synchronous transfer between the shuttle and the feeder buses. The research framework graph of the proposed methodology can be better described in Figure 1.  
Here, we provide Figure 2 in order to better explain the principle and scope of the proposed methodology. The study area has one rail station (M), two bus depots (D1 and D2), and five demand points (C1, C2,..., C5). Two schedules of the rail station are 7:15 and 7:20. Walking time for passengers from the drop-off point of the rail station to the subway platform is 3 min. There are  
Figure 1: Research framework.  
a number of boarding passengers located at each demand point with their time windows and a preferred subway schedule. For instance, at demand point C2 of Figure 2, we see 3; this means that three passengers will board the vehicle at this point. These passengers have preferred windows of service and subway schedules, i.e., [7:00, 7:05] and [7:05, 7:10] and 7:15. In the instance, two feasible DCR routes are yielded in the optimization process. Route 1 is illustrated by a solid line [D1(7:10)-C5(7:05)-C4(7:09)-C3(7:11)-M(7:16)] and Route 2 is also illustrated by a solid line [D2(7:02)-C2(7:04)-C1(7:07)-M(7:11)]. Take vehicle 2 as an example: The vehicle departs from D2 at the time of 7:02, and arrives at demand points C2 and C1 at the times of 7:04 and 7:07 to pick up three passengers and one passenger, respectively; finally, the vehicle returns back to M at 7:11. In this case, the ride-times of C2 and C1 are 7 min and 4 min, and the wait-time for both of them is 1 min. Thus, the total ride-time and wait-time for all passengers in vehicle 2 are \(3\times 7+1\times 4\) = 25 min and \(4\times 1\) = 4 min.  
The objective is to find a feeder bus routing and schedule that simultaneously minimizes the total travel time for all passengers, which includes two terms: the first term deals with riding time for passengers from pick-up locations to the rail station and the second one is related to wait-time for passengers taking the subway beforehand. To ensure that our methodology fits well with the real-world situations, the following assumptions should be considered:  
1. The pickup locations, the number of passengers, the boarding time window, and the predetermined subway schedule are collected by using a cell phone app.
2. The travel distance or time between demand points, bus depots, and rail stations in the real traffic network are easily obtained by using the Open GIS tool.
3. The demand point can only be visited by one feeder bus.