# Intelligent Traffic Signal Phase Distribution System Using Deep Q-Network
## 3 Proposed Model  
To identify the performance of the traffic signal system, there are three main factors at the intersection: throughput, queue length, and waiting time. Throughput represents the number of vehicles exiting from the intersection over a period of time. The traffic signal system needs to be optimized to process as many vehicles as possible during a period of time. The queue length refers to the number of vehicles waiting at an intersection. Finally, the waiting time represents the time taken to exit the intersection after the vehicle arrives at the intersection. Usually, the average of queue length or waiting time are used to determine the situation of the system. However, the average value can make it difficult to accurately analyze the situation at an intersection. This is because the average is the intermediate between the best and worst values. For example, if we focus only on reducing the length of the longest queue to lower the average value of the queue length at the intersection, the progress of vehicles in a short queue may be restricted. However, the standard deviation is a measure of the degree of variance of data to the mean. The standard deviation of the queue length represents information about the deviation between the lane where many vehicles wait within the intersection and the lane where fewer vehicles wait. Therefore, it is effective to compare and control the situation of each lane. The queue length and waiting time indicate the intersection. A long queue length indicates that many vehicles are waiting at the intersection. In addition, a large waiting time means that there are vehicles that wait for a long time. The queue length refers to the quantitative information of the vehicles, and the wait time is the temporal information of the vehicles. Therefore, depending on the signaling method, more meaningful factors differ. Thus, an experiment was conducted to determine which factors are important according to the signaling technique. A single intersection was assumed in the experimental environment. The experiments were conducted with the following reward parameters: throughput (tp), the combination of throughput and average queue length (tp + avgql), the combination of throughput and standard deviation of the queue length (tp + qlstd), the combination of throughput and average wait time (tp + avgwt), and the combination of throughput and standard deviation of the wait time (tp + wtstd). Figures 1 and 2 show the experiment results of the phase order allocation techniques. As shown in Figure 1, the technique of combining throughput and queue length-related  
elements, which are average queue length or standard deviation of queue length, has a smaller average queue length performance value than other techniques. In step 3, the technique of combining throughput and standard deviation of queue length shows about 20% shorter queue length than the combining technique of throughput and the standard deviation of wait time. In Figure 2, the average wait time is about 35% lower with the technique of combining throughput and queue length-related factors than when considering only throughput. It is also about 22% smaller than the performance of the wait time-related factor combination technique. Figures 3 and 4 show the experiment results of the allocation technique of the green light duration. As shown in Figure 3, the average queue length is similar in all techniques. In Figure 4, by contrast, the average wait time resulted in vehicles waiting less when the wait time-related factor was applied to the reward parameter. On average, the combination of throughput and wait time-related factors has about 35% less wait time than the combination of throughput and queue length-related factors. In the case of a signal control using an order allocation technique, the direction to which the next green signal is allocated is determined. The queue length factor is more meaningful than the wait time factor in allowing more vehicles to exit during a period of time.