## 8 Discussion
### Experiment 3: Versus Conventional Control Method  
We compared MD4-AQF against a conventional fully actuated signal control (FASC) method in terms of vehicle delay. The technical details of FASC can be found in [25]. Briefly, FASC extended current phases on a second-by-second basis, according to the detected time headways of all vehicles crossing a specific point on each approach lane. FASC typically utilizes data from inductive loop detectors that are widely deployed at real-world intersections. Such an actuated method has long been applied in traffic engineering. FASC has consistently served as a conventional baseline in many previous studies. Its real-time signal timing strategy could produce highly acceptable intersection performance. We reused the prepared 2000 traffic demand scenarios via the D-optimal design in the previous experiment. We also performed two simulation runs in each scenario, with signals timed by MD4-AQF and FASC, respectively. We recorded the average vehicle delay at the intersection for the following comparative analyses. As box plots in Figure 9 show, the medians of the average vehicle delay caused by MD4-AQF and FASC, across the 2000 traffic demand scenarios, were 49.62 s and 61.24 s, respectively. The proposed method achieved an 11.62 s (or 19.0%) advantage over FASC in terms of the median value. Moreover, it produced much lower values for both the top and bottom quartiles. Notably, the upper quartile (57.69 s) for MD4-AQF is even lower than the median (61.24 s) for the conventional method. These signified that the proposed method enabled the signals to operate with overall superior performance. On the other hand, the inter-quartile range (72.90 \(-\) 53.36 \(=\) 19.54 s) and whisker range (102.16 \(-\) 39.47 \(=\) 62.69 s) produced by FASC were comparatively wide, meaning that the conventional method resulted in less stable performance than MD4-AQF. In particular, there was an obvious contrast in the upper whisker (102.16 s versus 77.70 s). It was inferred that MD4-AQF expanded the intersection capacity and performed well in some severe demand scenarios. We then paired the delay data produced by two methods to draw the scatter plot in Figure 10. As shown, the proposed method led to better average vehicle delay than FASC in the great majority of demand scenarios. Such an advantage could be approximately 59 s or 46% in some scenarios. Whereas the conventional method outperformed MD4-AQF in very few scenarios with a relatively small difference in delay. Admittedly, there were still some traffic patterns in FASC's favor, suggesting its competitiveness as a method that has been widely applied over a long period. A potential direction for future work could be to develop a control mechanism that autonomously switches between the conventional method and MD4-AQF. We further analyzed the paired average vehicle delay from a statistical perspective. We first performed the Kolmogorov-Smirnov normality test with Lilliefors correction. The resulting statistic, D = 0.073 and P \(<\) 0.05, showed no normality in the difference in vehicle delay caused by MD4-AQF and FASC. Thus, we had to resort to the non-parametric substitute of the paired \(t\)-test, the Wilcoxon matched-pair signed rank test. The resulting statistic Z was \(-\)37.729, as illustrated in Table 2. There was a significant difference in the average vehicle delay at a significance level of 0.05. The number of negative and positive ranks was 1951 and 49, respectively. It meant that MD4-AQF surpassed FASC in terms of vehicle delay in 95.35% of the 2000 demand scenarios. According to the results of the simulation experiments, the proposed MD4-AQF method enabled an agent to acquire signal timing knowledge effectively. The agent improved the average vehicle delay from more than 130 s to less than 50 s during training. The comparison with another MFDRL method served as an ablation study. It showed that the innovative components in MD4-AQF led to faster, more stable, and more effective training with fewer network parameters.