# Traffic Signal Control with State-Optimizing Deep Reinforcement Learning and Fuzzy Logic
## 6 Experimental Results  
The experimental results are divided into seven parts. The first part is the results of the training process, and the remaining parts are the experimental results. Following the completion of the learning process, the results show the average value obtained from the experiment in a total of 25 episodes, which are different situations. The experimental results are for the three types of traffic light control.  
1. Traditional traffic light control is a method that is currently used worldwide, in which a green light signal is given for 10 s in a sequence and repeated for each arm, as shown in Figure 5. It is called the traditional method in the experimental results.
2. Traffic light control using a prototype Deep Q-network with fuzzy logic is used for comparison. In the experimental results, it is called the original DQN with the fuzzy logic method [29].
3. Traffic light control using the proposed method.  
In the experimental results table, ALL-4 indicates that there were four lanes in all outgoing lanes, E-3 indicates that the road coming east had three outgoing lanes, N-3 indicates that the road coming north had three outgoing lanes, S-3 indicates that the road coming south had three outgoing lanes, and W-3 indicates that the road coming west had three outgoing lanes.  
The experimental results in Sections 6.1-6.7 are compared with the traditional and original DQN with fuzzy logic. The following values were used to compare the results.  
1. The average total waiting time (WT\({}_{\text{AVG}}\)) is the average accumulated waiting time of all vehicles in the outgoing lane per step. \[\text{WT}_{\text{Total}}=\sum_{i=1}^{\text{N}}\text{WT}[i]\] (7) where N is the number of vehicles at the intersection in the outgoing lane at time step t, and WT is the accumulated waiting time of the vehicle. \[\text{WT}_{\text{AVG}}=\frac{1}{\text{T}}\times\sum_{i=1}^{\text{T}}\text{WT }_{\text{Total}}[i]\] (8) where T is the maximum step, and WT\({}_{\text{Total}}\) in Equation (7) is the total waiting time at time step t.
2. The average total waiting time for vehicles to make a left turn (WTL\({}_{\text{AVG}}\)) is the average accumulated waiting time for all vehicles in the outgoing lane to make a left turn per step. \[\text{WTL}_{\text{Total}}=\sum_{i=1}^{\text{N}}\text{WTL}[i]\] (9) where N is the number of vehicles at the intersection of the left-turn lane at time step t, and WTL is the accumulated waiting time of vehicles in the left-turn lane. \[\text{WTL}_{\text{AVG}}=\frac{1}{\text{T}}\times\sum_{i=1}^{\text{T}}\text{ WTL}_{\text{Total}}[i]\] (10) where T is the maximum step, and WTL\({}_{\text{Total}}\) in Equation (9) is the total waiting time of the vehicle on the left-turn lane at time step t.
3. The average total waiting time per car (WTC\({}_{\text{AVG}}\)) is the average accumulated waiting time per vehicle in the outgoing lane per step. \[\text{WTC}_{\text{AVG}}=\frac{1}{\text{T}}\times\sum_{i=1}^{\text{T}}\frac{ 1}{\text{Q}}\text{WTL}_{\text{Total}}[i]\] (11)where T is the maximum step, Q is the number of vehicles at the intersection with a velocity below 0.1 m per second, and WTTotal in Equation (7) is the total waiting time at time step t.