## 6 Traffic Simulation  
The system proposed in this paper requires data collection for clustering and classification. However, it is difficult to collect traffic data in a real environment. Therefore, we use the Vissim traffic simulator, which is widely used in transportation engineering for microscopic traffic simulation, to collect intersection traffic data and also to evaluate the performance of the proposed system. Figure 4 shows the intersection traffic environment configured in Vissim and also shows the traffic signal phases. A standard intersection model is used, which has three input lanes and two output lanes for each ramp way. The leftmost input lane is for left turning, and the center lane is for straight traffic. The far right lane is used for both straight and also for right turning with 20% probability. The traffic signal cycle at the intersection consists of four phases. The signal duration is set to be 27 s for straight traffic and 15 s for left turning traffic according to the traditional Webster's method [39]. On the other hand, the signal duration for yellow and red in each phase are set differently according to the traffic speed based on the FHWA's Traffic Signal Timing Manual [40]. Traffic flow includes car-following and lane change motion. Since Vissim provides two different models, called the _continuous decision model_ and _one decision model_, to mimic the reaction patterns of real drivers at an intersection when the traffic signal changes from green to yellow, we utilize both of these models in our simulations to generate a more realistic intersection traffic data. In a continuous decision model, there are two options available. First, a vehicle will not brake, if even the maximum deceleration would not allow for a stop at the stop line. Second, a vehicle brakes if a vehicle cannot pass the traffic light within 2 s when continuing at its current speed rate. On the other hand, in one decision model, the decision made at the time of the yellow onset is kept until the vehicle has passed the stop line. A vehicle stops according to the following probability  
\[p=\frac{1}{1+e^{-x_{1}-a_{2}v-a_{3}dx}} \tag{2}\]  
Figure 4: Intersection traffic simulation in Vissim. (**a**) Simulated intersection traffic; (**b**) Traffic signal phase. where \(v\) is the vehicle's current speed, \(dx\) is the DTI, and \(\alpha_{1}\), \(\alpha_{2}\), \(\alpha_{3}\) are fitting parameters. In our simulation, we use the default values for these fitting parameters, which are \(\alpha_{1}=1.59\), \(\alpha_{2}=0.27\), and \(\alpha_{3}=-0.26\) provided in Vissim. Figure 5 shows representative reaction patterns of traffic observed in simulation according to two decision models. Depending on the state of a vehicle such as current speed, DTI at the time of yellow onset, the vehicle reacts into three different patterns. First, \(Go\) is the case when a vehicle enters the intersection before the red signal, \(Stop\) is the case when a vehicle stops at the stop line on the red signal, and finally, \(RLR\) means the case when a vehicle is entering the intersection at the red signal [9]. Figure 5a shows the change in speed for each reaction of continuous decision traffic. The vehicle with Go reaction does not have a red signal before the distance to the intersection becomes 0 m. The vehicle with Stop reaction stops gradually with a yellow signal starting at a distance more than 60 m from the intersection. However, vehicles with the RLR reaction show that they start to accelerate rapidly between about 15 to 20 m before the intersection. Figure 5b shows the speed change for each reaction of one decision model. In one decision model, Go and Stop reactions are similar to those in the continuous decision model. On the other hand, one of the vehicles with RLR reaction maintains speed without significant change in its speed even when the yellow signal starts.