## 3 Research Methodology
### Mobility Simulator for Idling Control Process  
The basic concept and algorithm of automatic vehicle idling control are provided in Figure 3. There are two fundamental requirements for the algorithm: that is, the autonomous vehicle should be physically equipped with a communication device and the reference time should be set to be compared with the waiting time to execute automatic vehicle idling control. The reference time is supposed to be defined according to the various vehicle characteristics such as vehicle type, vehicle year, fuel type, etc., but this study adopted a specific value (i.e., 10 s) referenced from the existing works. Specifically, the mobility simulator consists of five steps from vehicle generation to vehicle idling identification and control. Most steps (i.e., solid box in Figure 3) can be realized by the autonomous vehicles themselves, such as speed, position, turning direction, vehicle idling control, etc., except one step (i.e., dashed box in Figure 3), which is sharing traffic signal information via V2I communication. Each step is explained as follows:  
Step 1: Vehicle generation  
Figure 3: Automatic vehicle idling control method. Vehicles are generated on the entering links at pre-determined headways depending on traffic demand. Step 2: Identification of vehicle idling situations  
The speed of individual vehicles is monitored at every simulation time and when their speed is 0 kph, which is when they stop before a stop line or join a queue and the idling condition occurs. Then, this study computes the time that the shockwave reaches stopped vehicles from the stop line at the intersection of interest, referring to the time for vehicles to be able to start to move. Step 3: Transmission of signal information through V2I communication  
Every time vehicle idling situation is identified, the traffic signal information such as cycle length, current and consecutive phases, phase sequence, etc., is checked to determine if the automatic vehicle idling control function should be activated or not. Step 4: Determination of vehicle idling control  
At first, if the transmitted signal phase is not compatible with the turning direction of idling vehicles, the vehicle idling should be controlled. On the other hand, in case the signal phase matches the turning direction of idling vehicles and the phase is same as the reference time (i.e., Ref. time in Figure 3) or more, if the shockwave arrival time to the idling vehicles (i.e., time to start to move) is same as the reference time or less, the vehicle idling is controlled as well. Step 5: Estimating GHG emissions reciprocally linked to emission simulator  
At every simulation time, all individual vehicles resort to the emission simulator to calculate the CO2 emissions corresponding to operation modes such as braking, idling, and running. Later, aggregated CO2 emissions associated with scenarios with or without an automatic vehicle idling control function are compared to see the environmental benefits of the proposed function. There are two types of scenarios depending on the automatic vehicle idling control of an autonomous vehicle under C-ITS. One is no idling control (i.e., Figure 4a), and the other is vehicle idling control considering the queue length, time to start, reference time, and traffic signal information transmitted through V2I communication (i.e., Figure 4b). More specifically for Figure 4b, VISSIM observes all trajectories of individual vehicles at every simulation time and compares the waiting time and signal phase corresponding to the designated turning direction when stopping at the intersection until the simulation is terminated.