# A Division-of-Labour Approach to Traffic Light Scheduling
## 5 Results and Discussion  
Table 1 shows the results of the parameter optimisation process followed for finding a value for \(c\) for the division-of-labour algorithm. Performance degrades as the value for \(c\) increases from 1 to 5, after which performance improves, as the value for \(c\) increases from 5 to the most optimal value, 35. Performance degrades again as the value for \(c\) increases from 35 to 50. The value for \(c\) has no significant impact on the average vehicle travel time. Figures 5, 7, 9, 11, 13 and 15-17 show smoothed graphs of the trimmed average delay, along with their standard deviations after the static, Webster, max pressure, DDPG, DQN, and division-of-labour-based traffic scheduling algorithms were applied to the scenarios. In these figures, the solid lines indicate the average delay and the color ranges indicate the standard deviations. Figures 6, 8, 10, 12 and 14 show box plots of the average vehicle travel time for scenarios one to five. Travel time results were excluded for scenarios six, seven, and eight due to almost identical performances by the different traffic controllers. This is a result of the larger grid reducing the effect on average travel time by the controllers. Figure 4: An example of an irregular four-way intersection in the second intersection layout; green indicates a green traffic light for traffic that may go, and red indicates a red light for traffic that has to stop. Figure 5 shows that, in terms of delay, the max pressure algorithm performed best in the scenario with a constant low-traffic intensity in the first intersection layout. The division-of-labour and static algorithms both performed second best, and the Webster, DQN, and DDPG algorithms performed fourth, fifth, and sixth best, respectively. Max pressure was best able to account for variations in the traffic which become more significant when there is sparse traffic. The reinforcement learning algorithms were the least capable of accounting for these variations. Figure 6 shows that, in terms of travel time, the max pressure algorithm performed the best in scenario one because of the dynamic nature of the algorithm. The static, division-of-labour, and Webster algorithms performed second, third, and fourth best, respectively, whereas the reinforcement learning algorithms performed the worst. The DDPG and DQN algorithms performed worst, as both were trained to minimise delay instead of travel time. Figure 7 shows that, in terms of delay, the max pressure algorithm performed best in the scenario with a constant high-traffic intensity in the first intersection layout. The division-of-labour and static algorithms performed second best, and the Webster algorithm performed fourth best. The DDPG and DQN algorithms were both unable to generalise to the high traffic intensity after training. Figure 8 shows that, in terms of travel time, the \begin{table}
\begin{tabular}{c c} \hline \hline c & **Average Vehicle Delay** \\ \hline
1 & 816.1956 \\
5 & 831.2264 \\
10 & 829.6111 \\
15 & 818.5456 \\
20 & 810.5541 \\
25 & 802.7875 \\
30 & 795.0609 \\
35 & 782.9047 \\
40 & 789.7331 \\
45 & 811.7620 \\
50 & 829.0596 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results after grid search optimisation for the parameter of the division-of-labour traffic scheduling algorithm. Figure 5: Average vehicle delay during the constant low-traffic simulation (scenario one). algorithms performed similarly, with the max pressure algorithm performing slightly better than the other algorithms. Figure 9 shows that, in terms of delay, the max pressure algorithm performed best in the traffic scenario simulating a \"rush hour\" in the first intersection layout. The DDPG algorithm was able to generalise well after training and performed second best, while the division-of-labour algorithm performed third best. The high levels of overlap suggest an insignificant difference in performance between DDPG and the division-of-labour algorithm.