A Division-of-Labour Approach to Traffic Light Scheduling

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Traffic light scheduling optimisation using a task allocation model based on division-of-labour behaviour as observed in insect colonies.

Abstract

Traffic light scheduling is a critical aspect of traffic management with many recently developed solutions that incorporate computational intelligence approaches. This paper presents a traffic light scheduling algorithm based on a task allocation model that simulates the division of labour among insects in a colony, specifically ant colonies. The developed algorithm switches the green light based on a probability calculated every second from the traffic volume around the traffic light. The application of this algorithm to several benchmark simulated traffic scenarios shows optimal performance compared to five other traffic scheduling algorithms.

1. Introduction

Much of the productivity of modern society has become dependent on transport. The efficient management of traffic plays a particularly important role in the transport industry and, to an extent, society. Poor traffic management can cause accidents, and productivity is reduced by the resulting congestion. A study in Ghana found that traffic congestion reduced worker productivity by 9% per workday [1]. It is also estimated that 27% of global warming has been caused by transportation [2].

One of the most important aspects of traffic management, especially in urban areas, is traffic light scheduling. Many traffic light scheduling algorithms have been developed, as reviewed in [3,4,5], and newly developed algorithms tend to incorporate computational intelligence approaches to accommodate for the dynamic nature of traffic [6,7,8,9]. Despite the availability of smart traffic light scheduling algorithms, it is still the case that static and deterministic timing schedules are utilised that do not take the dynamic nature of this optimisation problem into consideration. This is mainly due to the ease of implementation of these static approaches and the little demand for software and hardware resources.

This paper presents a flexible and efficient model based on the division of labour within ant colonies [10] for the traffic light scheduling problem. The dynamic self-organising behaviour seen in the division of labour in insect colonies makes models of division of labour for task allocation an ideal approach to cope with the dynamic nature of the traffic light scheduling problem. In addition, the task allocation models of division of labour are very simple to understand and implement. The proposed traffic scheduling algorithm is applied to eight different traffic scenarios. The effectiveness of the algorithm is assessed by comparing the performance of this algorithm to the performances of five other traffic scheduling algorithms. The developed division-of-labour algorithm and another dynamic algorithm, the max pressure algorithm [11], generally performed best across these scenarios.

The remainder of the report is structured as follows: Section 2 provides background on traffic signal control and division of labour in insect colonies. The division-of-labour approach to traffic light scheduling is proposed in Section 3. Section 4 describes the empirical procedure followed to analyse the performance of the division-of-labour traffic light scheduling model. The results are presented and discussed in Section 5.

2. Background

This section provides background on traffic signal control and existing solutions in Section 2.1. Division of labour in insect colonies is discussed in Section 2.2.

2.1. Traffic Signal Control

Traffic light control consists of showing a combination of signals that allow certain pre-defined movements of vehicles at traffic intersections from incoming lanes to outgoing lanes for a chosen period of time and disallowing other movements. A phase refers to a specific combination of movement signals that allows nonconflicting traffic movements. A cycle refers to a cyclic sequence of all possible phases of an intersection.

The simplest approach to traffic light control is the static controller, which allocates the same fixed amount of time to every phase in a cycle. This approach is stable but generally not efficient because the fixed timings prevent the controller from adapting to changing traffic distributions.

The Webster method [5] is a widely used adaptive traffic light scheduling algorithm. After a predefined period of time, it calculates a cycle length and splits the cycle length between the phases based on the volume of traffic since the last calculation. The calculation uses the time lost for every phase change, including the acceleration of any stationary vehicles, the number of cars travelling through the intersection, and the saturation flow rate. The saturation flow rate is defined as the highest amount of vehicular flow possible. It can be proved [5] that the Webster method minimises the travel time of vehicles passing through an intersection when the traffic distribution is uniform.

The max pressure traffic light scheduling algorithm [11] is a delay-related algorithm designed to reduce the risk of over-saturation at a traffic intersection by minimising the “pressure” of an intersection. The “pressure” of a phase is defined as the difference between the number of vehicles in the incoming lanes and the number of vehicles in the corresponding outgoing lanes. It can be proved [11] that max pressure maximises the throughput of a road network when all intersections use this algorithm.

Wei et al. [5] presented an overview of classical traffic scheduling algorithms that have been successfully deployed to real-world traffic. The paper talks about the deterministic timing-based Webster algorithm, the offset-based GreenWave and Maxband algorithms, the rule-based actuated control, self-organising traffic lights (SOTL), and the Sydney coordinated adaptive traffic system (SCATS) algorithms, as well as the dynamic max pressure algorithm.

Yau et al. [8] presented six algorithms utilising reinforcement learning of some form. Reinforcement learning [12] is a machine learning paradigm where a model, referred to as an agent, learns what actions are most optimal to accomplish a specific task in a given environment through a trial-and-error-based learning process. A more in-depth discussion of reinforcement learning is beyond the scope of this paper, but further detail can be found in [13]. Genders and Razavi [14] implemented traffic scheduling algorithms that utilise the deep Q-network (DQN) [15] and deep deterministic policy gradient (DDPG) [16] reinforcement learning algorithms that also utilise neural networks.

Actuated control-based traffic scheduling algorithms are a broad range of real-time algorithms that utilise sensors and complex sets of rules. Most modern traffic scheduling algorithms in urban areas, such as SCATS and SCOOT [17], are considered actuated control. A more comprehensive review of modern actuated control-based traffic scheduling is beyond the scope of this paper, but more information on these approaches can be found in Eom et al. [18].

Simulation of urban mobility (SUMO) [19] is an established open-source program for traffic simulation. Useful features of this simulator include being able to apply custom traffic light scheduling algorithms to traffic lights and importing real-world road networks from OpenStreetMap (https://www.openstreetmap.org (accessed on 1 July 2023)). Genders and Razavi [14] developed a Python framework for the development and evaluation of adaptive traffic signal control models.

García-Nieto et al. [20] developed a traffic scheduling algorithm that implements particle swarm optimisation.

2.2. Division of Labour in Insect Colonies

The ecological success of many social insects has been attributed to the self-organised, self-adaptive, and distributive division of labour among the individuals of these social systems [21]. Division-of-labour occurs in a social biological system when all of the individuals of that system (e.g., a colony) are co-adapted through divergent task specialisation, such that there is a fitness gain as a consequence of such specialisation [22]. Various tasks occur within insect colonies, including reproduction, brood care, foraging, waste disposal, defence, cemetery organisation, and nest construction, amongst others. Task allocation and coordination occur without any central control; they are the result of self-organisation and self-adaptation. Individuals respond to simple local cues, for example, the pattern of interactions with other individuals or pheromone droppings by other individuals [23]. The task allocation is dynamic, based on external or internal stimuli. Despite task specialisation, task switching does occur, resulting in ratios of workers that perform different tasks, which vary over time. Variations in these ratios are caused by internal perturbations or external environmental conditions, e.g., changes in climate, food availability, and predation. For interest, Eugene N. Marias was the first to report observations of such task switching [24]. Very important to the survival of certain termite species is the maintenance of underground fungi gardens. During a drought, termites are forced to transport water over very large distances to feed the gardens. During such times, all worker termites, including the soldiers, have been observed to perform the task of water transportation. Not even in the case of intentional harm to the nest structure do the ants deviate from the water transportation task. In less disastrous conditions, soldiers will immediately appear on the periphery of any “wounds” in the nest structure, while worker ants repair the structure.

It is this self-organised, dynamic, and distributed division of labour in nature that lends it to applications of multi-task decision-making problems that can be solved by multiple artificial agents.

Bonabeau et al. [10] developed a single task allocation model that simulates the division-of-labour behaviour among insects in colonies. The model works by assigning every ant a response threshold and every task a stimulus level based on the intensity of the stimuli of the task. The response threshold of an ant is the likelihood of the ant to react to the stimuli associated with a task. An ant will perform a task with high probability if the stimulus of the task exceeds the threshold of the ant. The stimulus level of a task increases at a fixed rate the longer it is not satisfied. The stimulus level of a task decreases when an ant performs that task.

The model lets an ant k perform a task j with a probability indicated by

$$P_{kj}(X=0\to X=1)={\displaystyle \frac{s_j^2}{s_j^2+{\theta }_{kj}^2}}$$

(1)

where X is the state of the ant ($X=0$ indicates inactivity with respect to task j, and $X=1$ indicates active performance on task j). The variable $s_j$ indicates the stimulus value of task j, and ${\theta }_{kj}$ indicates the response threshold of ant k towards the task j.

An active ant will become inactive with respect to task j with probability p, i.e.,

$$P_{kj}(X=1\to X=0)=p$$

(2)

Therefore, on average, an ant will spend $1/p$ time units working on the task.

The stimulus intensity of task j is calculated as

$$s_j(t+1)=s_j\left(t\right)+\delta -\alpha n_{act}$$

(3)

where $\delta$ is the increase in stimulus intensity over time, $\alpha$ is the work efficiency of the ants, and $n_{act}$ is the number of active ants.

Campos et al. [25] applied a method for assigning resources based on this variant of the single task-allocation model to a dynamic flow shop scheduling problem. Klazar [26] developed an algorithm inspired by the division of labour in ant colonies for the dynamic allocation of tasks in distributed computing.

3. Division-of-Labour Model for Traffic Light Scheduling

The developed division-of-labour-based traffic scheduling algorithm is designed for use in a complex intersection with multiple traffic phases. The single task-allocation model is used where the next traffic phase in the cycle is represented as the task.

The probability of the traffic phase changing every second is calculated as

$$P=\left\{\begin{array}{cc}{\displaystyle \frac{{(\overline{s}\times s_f)}^{\omega }}{{(\overline{s}\times s_f)}^{\omega }+{(\frac{\theta }{\overline{s}+\theta }\times L+\theta \times s_f)}^{\omega }}}\hfill & \mathrm{if}s+\theta \ne 0\hfill \\ 0\hfill & \mathrm{if}s+\theta =0\hfill \end{array}\right.$$

(4)

where $\overline{s}={\displaystyle \frac{s}{n-1}}$ and $\omega =2+{\displaystyle \frac{s+\theta }{c}}$. The number of traffic phases in the cycle is represented as n. The number of stationary vehicles waiting for the traffic phase to change is represented as s, and $\theta$ is the number of vehicles that will become stationary if the traffic phase were to change. The saturation flow rate is represented as $s_f$, and L is the time lost when the traffic phase changes, which includes the yellow light duration in seconds, the number of seconds where all traffic lights are red, and the time lost while the vehicles accelerate. The variable c is a parameter that sets how sensitive the steepness threshold is to the total traffic volume around the intersection.

The variables $\overline{s}$ and $\theta$ are scaled with the saturation flow rate $s_f$ to allow these variables to be compared to the time lost when the traffic phase changes, L. The variable $\overline{s}$ represents the average number of vehicles per phase not currently allocated the green light. The stimulus value, $s_j$, in Equation (1) is thereby set as $\overline{s}\times s_f$, the time needed to clear the average traffic volume in a phase not currently allocated the green light.

The variable L is scaled with ${\displaystyle \frac{\theta }{\overline{s}+\theta }}$ so that the effect of L is proportional to the ratio of the number of vehicles shown the green light, and the average number of vehicles per phase not shown the green light. The threshold value, ${\theta }_{kj}$, in Equation (1) is thereby set as ${\displaystyle \frac{\theta }{\overline{s}+\theta }}\times L+\theta \times s_f$, a representation of the time lost if the traffic phase is changed.

A dynamic steepness threshold, $\omega$, is used to prevent the traffic phase from constantly changing in high-intensity traffic scenarios and allow for some flexibility in lower-intensity traffic scenarios. It was found that a linear relationship exists between the total amount of traffic around the intersection and the most optimal value for $\omega$, so $\omega$ is set to be linearly proportional to the total amount of traffic around the intersection, $s+\theta$. Two is added to ${\displaystyle \frac{s+\theta }{c}}$ so that $\omega$ starts from the default steepness threshold value of two as the total traffic volume increases from zero.

The use of probability in every time unit to determine whether the controller should continue to the next phase in the cycle or not is what distinguishes this approach from existing approaches. The developed division-of-labour-based traffic scheduling algorithm is formally described in Algorithm 1. Every timestamp of the phase has a probability P of not changing, a minimum green light duration, $t_{\min }$, and a maximum green light duration, $t_{\max }$.

Algorithm 1 Division-of-Labour-Based Traffic Scheduling Algorithm

input: current phase duration t, minimum phase duration $t_{\min }$, maximum phase duration $t_{\max }$ for every timestamp do       $t=t+1$       if $t\ge t_{\min }$ then             r = random number between 0 and 1             For each traffic phase, calculate P as in Equation (4)             if $P>r$ or $t\ge t_{\max }$ then                  Set current phase to the next phase in the cycle                  $t=0$             end if       end if end for

It should be noted that the computational cost of the division-of-labour algorithm is not significant. Most of the cost relates to the calculation of Equation (4), which is a simple calculation for the probability of a traffic phase change for each traffic phase. This results in a $O\left(n\right)$ calculation per time step. Sampling of the resulting probability distribution is also computationally efficient, as illustrated in Algorithm 1, requiring sampling of a random value for each traffic phase. Again, this results in $O\left(n\right)$ computational cost, with the overall cost per time step also being $O\left(n\right)$.

4. Empirical Procedure

The developed division-of-labour-based traffic scheduling algorithm was tested against the static, Webster, and max pressure algorithms, as well as the DQN and DDPG-based reinforcement learning algorithms. These algorithms were selected for their applicability to isolated intersections. The static and Webster algorithms were chosen for their ability to handle constant streams of traffic, and the max pressure algorithm was chosen for its ability to handle changing streams of traffic. Furthermore, these three algorithms were also chosen for being established from their frequent use in practice. The DQN and DDPG-based algorithms were chosen for their potential performance gains from the usage of reinforcement learning and neural networks.

All simulations simulated six hours of traffic on one of two intersection layouts. The first intersection layout consisted of a three-by-three grid of identical complex four-way intersections, as visualised in Figure 1. An individual intersection in this layout can be visualised in Figure 2. The first phase of the cycle of these intersections consisted of north-to-east and south-to-west moving traffic, and the second phase of the cycle consisted of north-to-south and south-to-north moving traffic. The third phase of the cycle consisted of west-to-north and east-to-south moving traffic, and the fourth phase of the cycle consisted of east-to-west and west-to-east moving traffic. Every road connected to the intersection consisted of three separate lanes. For this intersection layout, the algorithms were evaluated on five scenarios with different traffic characteristics:

• Scenario One: Low traffic was constant in all directions, with an average of three vehicles entering the simulation every five seconds. This scenario tested the efficiency of an algorithm when controlling low amounts of traffic.
• Scenario Two: High traffic was constant in all directions, with an average of three vehicles entering the simulation every second. This scenario tested the ability of an algorithm to handle high amounts of traffic.
• Scenario Three: Traffic intensity in all directions was scaled by $sinx$, where $x={\displaystyle \frac{t\pi }{\mathrm{21,600}}}$ and t was the elapsed time since the simulation started in seconds. This scenario tested the ability of an algorithm to handle varying levels of traffic that models a “rush hour”.
• Scenario Four: Every incoming lane had a traffic intensity scaled by $sinx$, where $x={\displaystyle \frac{kt\pi }{\mathrm{21,600}}}$ and k is unique to every incoming lane and $k\in \{7,8,9,10,11,12\}$. This scenario tested the ability of an algorithm to handle fluctuating traffic where traffic intensity varies across the grid.
• Scenario Five: Traffic was scaled as in Scenario Four, but the roads between traffic lights were half the length. This scenario tested the ability of an algorithm to handle traffic in a smaller network.

The second intersection layout was an irregular layout modelled after a section of the road network in the town of Stellenbosch (South Africa), as visualised in Figure 3. Unlike the first intersection layout, the intersections are not identical and have cycles with traffic phases determined by the number of lanes entering either side of the intersection. An example of one of these intersections is visualised in Figure 4. Vehicles were allowed to enter and leave the simulation from the main roads and a cul-de-sac in the centre of the intersection layout. For this intersection, the algorithms were evaluated on three scenarios with different traffic characteristics as follows:

• Scenario Six: Low traffic was constant from all areas that vehicles could enter from. This evaluated the efficiency of an algorithm when controlling low amounts of traffic in an irregular intersection layout.
• Scenario Seven: High traffic was constant from all areas that vehicles could enter from. This evaluated the ability of an algorithm to handle high amounts of traffic in an irregular intersection layout.
• Scenario Eight: Traffic intensity was scaled by $sinx$, where $x={\displaystyle \frac{t\pi }{\mathrm{21,600}}}$ and t was the elapsed time since the simulation started in seconds. This scenario evaluated the ability of an algorithm to handle varying levels of traffic that models a “rush hour” in an irregular intersection layout.

A saturation flow rate of 0.38 was assumed for all simulations. The yellow light duration was set to two seconds, and the duration for which all traffic lights are set to red when changing phases was set to three seconds. The Webster, max pressure, and developed division-of-labour algorithms use a minimum green light duration of seven seconds to prevent extremely short green light durations. A maximum green light duration of 60 s is enforced on the Webster and division-of-labour algorithms to prevent scenarios where traffic scenarios with low traffic demand are never given time.

With respect to the Webster algorithm, the cycle duration has a minimum of 38 s and a maximum of 250 s, and timing is recomputed every 450 s. The static uniform algorithm has green light durations that depend on the scenario to which it is applied. The durations for a scenario are calculated by applying the Webster algorithm to the point in the scenario with the highest traffic volume. An algorithm was applied to every scenario 30 times, and the average vehicle delay and travel time caused by the algorithm were recorded over the 30 independent runs.

A value for the c parameter of the division-of-labour-based traffic scheduling algorithm, which sets how sensitive the steepness is to the total traffic volume around the intersection, was found through a grid search before any algorithms were applied to simulations. It was found that values for c smaller than one lead to poor performance, and values much larger than 50 lead to poor performance as well. For those reasons, the average vehicle delay was taken across 30 independent runs after applying the division-of-labour algorithm to Scenario Four, with values of c between and including 1 and 50. Scenario Four was chosen for the variety of traffic intensities that arise.

5. Results and Discussion

Table 1. Results after grid search optimisation for the parameter of the division-of-labour traffic scheduling algorithm.

c	Average Vehicle Delay
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

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 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 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. 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 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.

Figure 13 and Figure 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 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 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. The DDPG and DQN algorithms were both unable to generalise after training. Given the performances of the static and Webster algorithms relative to the division-of-labour algorithm in the first intersection for the constant high-traffic intensity scenario, it was expected that these algorithms would perform better.

Figure 17 shows the performances of the algorithms applied to the traffic scenario simulating a "rush hour" in the second intersection layout. The max pressure and division-of-labour algorithms performed first and second best, respectively. The static and Webster algorithms performed third best. The DDPG and DQN algorithms were both unable to generalise after training.

6. Conclusions

Eight different traffic scenarios were applied to a developed traffic scheduling algorithm based on the division of labour in insect colonies, along with the static, Webster, max pressure, and two reinforcement learning-based traffic scheduling algorithms. Of the algorithms that could handle all scenarios, the division-of-labour algorithm performed best. The max pressure algorithm performed best in the scenarios the algorithm could be applied to but is not suitable for smaller road networks. Furthermore, max pressure has the weakness of not accounting for the waiting time of vehicles, and scenarios can arise where the max pressure algorithm causes some vehicles to wait for long periods of time. The DQN algorithm was not able to generalise to the training scenarios after training. The DDPG algorithm generally performed well but also did not generalise to scenarios with high traffic intensities.

Many other traffic light scheduling algorithms exist that utilise reinforcement learning [8], and future work can compare some of these algorithms to the developed division-of-labour algorithm. Future work can also compare the performance of the developed division-of-labour algorithm to algorithms that optimise the offsets between fixed timing algorithms in a network of intersections, like the GreenWave and Maxband algorithms [5].

Traffic light scheduling is ultimately a multi-objective optimisation problem. This paper reported the results of two objectives, i.e., minimisation of delay and travel time, individually. Ultimately, the traffic light scheduling problem is a dynamic multi-objective optimisation problem. Future work will expand the division-of-labour model to a multi-objective division-of-labour algorithm.