## 7 Experiments
### Experiment 2  
FACT uses logic rules to solve the single-ring RISC problem. Its goal is to finitely extend current vehicle phase to serve its continued demand. As required by RiLSA [54], a vehicle detector is placed on each approach lane, \(dp\) meters upstream of the stop line, to detect time headways. The current vehicle phase ends if either of the following conditions is met: (1) all the detectors of the phase have detected a headway greater than \(gt\) seconds after the expiration of its minimum green; and (2) the phase reaches its maximum green. \(gt\) is known as the \"gap time\". RiLSA requires the value of \(gt\) to be between 2 s and 3 s during peak periods. In this study, we conduct the experiment with \(gt\) being set to 2.0 s, 2.5 s, and 3.0 s, respectively. In addition, RiLSA requires the value of \(dp\) to be set to the product of \(gt\) and the posted speed limit. This is to allow the last vehicle triggering the detector to approach the stop line before the end of green [54]. With the lane-by-lane detectors, FACT essentially employs the time-series data of each vehicle's headway. Actually, FACT constructs a point-based \"state representation\" in a sense. Compared with the grid-based representation in D3 ynQN, FACT in a way also fully exploits the information of every vehicle. Given that the geometric design and the phase sequence are fixed over time, the average vehicle delay is governed by the traffic demand and the signal operations. So we controlled the building elements of the traffic demand to investigate the impacts of TA and FACT on the average vehicle delay. The controlling factors and their levels are given as follows. 1. The vehicle volume on each intersection approach (veh/h): 1200, 1210,..., 1500. Figure 5: Training curve of the agent. Solid line represents the 50 th percentiles of the average vehicle delay across the 50 simulation runs in each test, and shaded area covers the 15–85 th percentiles. The left-turn ratio on each intersection approach (%): 15.0, 15.2,..., 25.0. The right-turn ratio on each intersection approach (%): 5.0, 5.2,..., 10.0. The unidirectional pedestrian volume on each crosswalk (ped/h): 100, 110,..., 150. Considering the number and levels of controlling factors, we performed a D-optimal design [55] by using Ngene 1.1.1. For each value of gap time, a total of 2000 demand scenarios were generated for the intersection. The D-error was \(1.3\times 10^{-5}\). For each demand scenario, we executed four simulation runs, with the signals being timed by TA, and by FACT with different gap times, respectively. The average vehicle delay was measured from 600 sim.s to 4200 sim.s. The distributions of the data measured are presented in box plots. As shown in Figure 6, the 25 th, 50 th, and 75 th percentiles of the average vehicle delay were unexceptionally lower at the TA-enabled intersection than at the FACT-enabled ones, regardless of the gap times. It implied that TA allowed the intersection to operate with generally better performance. On the other hand, the differences in the inter-quartile ranges and whisker ranges indicated that more stable performance could be achieved at the TA-enabled intersection. We draw a scatter plot to investigate the average vehicle delay at the TA-enabled and FACT-enabled intersections in each demand scenario. As shown in Figure 7, the average vehicle delay was smaller at the TA-enabled intersection than at the FACT-enabled one in the vast majority of demand scenarios with any gap time. The advantage of the TA-enabled intersection could be 10 s or greater, whereas the disadvantage of the TA-enabled intersection was ignorable. Figure 6: Box plots of the average vehicle delay at the TA-enabled and FACT-enabled intersections with different gap times. We conducted a paired samples \(t\)-test at the significance level of 0.05 to investigate the average vehicle delay at the TA-enabled and FACT-enabled intersections. As shown in Table 3, the mean of the average vehicle delay was 42.98 s at the TA-enabled intersection.