# A Division-of-Labour Approach to Traffic Light Scheduling
## 5 Results and Discussion
The Webster and static algorithms performed the fourth best, with the Webster algorithm performing slightly better as the traffic intensity increased. The DQN algorithm was again unable to generalise after training. Figure 10 shows that, in terms of travel time, the max pressure and division-of-labour algorithms performed the best in scenario three because of their dynamic nature. The Webster and static algorithms performed third and fourth best, respectively, whereas the DDPG algorithm performed worst due to being trained to minimise delay instead of travel time. Figure 6: Average travel time during the constant low-traffic simulation (scenario one). Figure 7: Average vehicle delay during the constant high-traffic simulation (scenario two). Figure 11 shows that, in terms of delay, the max pressure algorithm performed best in the traffic scenario where every incoming lane was allocated a different varying traffic intensity because of the dynamic nature of the algorithm. The division-of-labour, DDPG, and Webster algorithms performed second best, with the Webster algorithm performing slightly worse at the beginning and end of the simulation. The static algorithm performed worst because of the inability of the algorithm to adapt to changing traffic distributions, and the DQN algorithm was again unable to generalise after training. Figure 12 shows that, in terms of travel time, the max pressure algorithm performed best because of the dynamic nature of the algorithm. The division-of-labour, DDPG, and Webster algorithms performed second best, and the static algorithm performed fifth best. This is the only scenario where DPPG performed decently in terms of travel time. Figures 13 and 14 show that, in terms of both delay and travel time, the division-of-labour algorithm performed the best in the scenario simulating a smaller road network, with slightly better performance than the static and Webster algorithms. Both the DQN and DDPG algorithms were unable to generalise after training. The max pressure algorithm was unable to effectively handle the traffic in this scenario. This can be attributed to the  
Figure 8: Average travel time during the constant high-traffic simulation (scenario two). Figure 9: Average vehicle delay during the ”rush hour” simulation (scenario three). fact that the smaller road lengths result in the outgoing lanes of traffic lights also being incoming lanes of adjacent traffic lights, and vice versa. Less effective pressure calculations are, therefore, made when queues form in incoming lanes. Figure 15 shows that the max pressure and DDPG algorithms performed best in the scenario with a constant low-traffic intensity in the second intersection layout. The division-of-labour algorithm performed third best, and the static and Webster algorithms performed fourth best. The max pressure, DDPG and division-of-labour algorithms perform the best because of their dynamic nature, which allows these algorithms to account for variations in the traffic distribution, which become more significant when there is sparse traffic and enables these algorithms to be applied to the intersections with different shapes, as found in the second intersection layout. Despite the generally lower intensity of traffic, the DQN algorithm was again unable to generalise because of the variations in traffic distribution caused by the irregular intersection layout. Figure 11: Average vehicle delay during the fluctuating traffic simulation (scenario four). Figure 10: Average travel time during the “rush hour” simulation (scenario three). Figure 14: Average travel time during simulation in the smaller network (scenario five). Figure 12: Average travel time during the fluctuating traffic simulation (scenario four). Figure 5:0 Average vehicle delay during simulation in the smaller network (scenario five). Figure 16 shows that the max pressure and division-of-labour algorithms performed first and second best, respectively. The static and Webster algorithms performed third best, with the static algorithm performing slightly better towards the end.