1. Introduction
Traffic congestion is a phenomenon with a large impact around the world [
1,
2,
3]. In the United States alone, cities such as Chicago, Boston, and New York have recorded the highest levels of congestion worldwide, with consequences for public health, induced by pollutant emissions, stress, and the time spent by drivers in traffic congestion [
4,
5,
6,
7]. Mexico City ranks fourth in traffic congestion and also faces the variety of social problems derived from this phenomenon [
7,
8,
9]. Traffic congestion also generates significant economic losses [
10], for example, in the USA, the cost of traffic congestion resulted in a loss of
$74 billion nationwide [
7,
11]. By 2030, this phenomenon is expected to be present in many more cities due to the growth of the population and in the use of vehicles [
12,
13].
To reduce vehicle congestion at intersections, control of traffic lights is necessary [
14,
15]. However, the normal use of this technology, with fixed-time (FT) phases, cannot be very efficient because this strategy cannot respond to changing traffic situations [
16]. The addition of sensors [
17], allowed the design of adaptive traffic signal control (ATSC) systems [
18]. During the early years of ATSC implementations, several techniques were proposed to optimize vehicular traffic. Among the most important are split cycle offset optimization technique (SCOOT) [
19], self-organizing traffic lights (SOTL) [
20,
21,
22], real-time hierarchical optimized distributed and effective system (RHODES) [
23], and Sydney coordinated adaptive traffic system (SCATS) [
24], which were attempts to set the timing of traffic lights more efficiently. Although these techniques were functional during the 1980s and 1990s, they are not adequate to deal with the more complex scenarios that arise with increasing vehicular traffic.
Artificial intelligence (AI) has significantly improved the performance of ATSC. Since 2015, there are more than 2500 publications related to ATCS, including mathematical modeling and AI applications [
25]. Techniques such as fuzzy Logic (FL) or Genetic Algorithms (GAs) have helped to reduce traffic congestion by designing more intelligent phase-timing patterns of traffic lights [
26,
27]. Other new AI techniques based on machine learning (ML) are also used. In particular, a widely used subset is deep learning (DL), which has achieved important advances in the area of vehicular traffic [
28]. Deep reinforcement learning (DRL) arises from the combination of DL with reinforcement learning (RL) algorithms that are used in the learning stage [
29,
30]. RL incorporates neural networks (NN) that, considering vehicle demand, identify characteristics of traffic behavior that are very helpful in phase-timing design [
31,
32,
33,
34].
In general, DRL techniques can be classified as centralized, where a set of traffic lights communicate and provide feedback between them for better decision making [
35], and decentralized, where traffic lights act independently of each other [
36]. There is also research that proposes hybrid solutions using both paradigms [
37]. Due to the expected increase in the number of connected and automated vehicles (CAVs), which do have a different interaction with infrastructure or vehicular traffic, analysis of technologies to control intersections also allows the proposal of behaviors that would not be possible in regular scenarios [
38].
The complexity of DRL techniques in ATSC is related to the size of the traffic network to be analyzed and the intrinsic difficulties of the algorithmic implementation of the chosen DRL model. Complexity is greater in centralized techniques because they manage several intersections simultaneously. The results obtained to date indicate that there are still pending issues, such as long execution times, convergence problems, and the large number of variables to be considered, that limit their application to real situations [
31,
33,
39,
40,
41]. There are DRL techniques that have been successfully applied to a set of single intersections. However, the results reported correspond to cases where intersections and traffic conditions are similar [
42,
43].
Single intersection studies use variables such as queue length, waiting time, vehicle spacing, specific vehicle type, or number of vehicles approaching the intersection as reference information and work with the complexity of traffic and the given choice of variables [
31]. They usually take traffic lights at the intersection as a single global agent [
44]. The research in [
27,
45,
46], shows a number of works where optimization is solved with metaheuristic-based algorithms.
Although most ATSC studies with DRL treat intersections as exclusive global agents or apply decentralized strategies to multiple intersection systems [
47,
48,
49,
50], few of them deal with the agent "anxiety" to prematurely change phase with small stochastic variations. Some studies use a decentralized approach at single intersections, modeling each traffic light as an independent agent and including the number of traffic light changes (flickers) as a specific variable [
51]. This approach could allow better local coordination and traffic stability by solving the convergence problems that constrain traditional models, such as excessive changes in traffic lights that can affect traffic safety and stability [
52].
It is still necessary to apply DRL models in single intersections with the intention of correcting erratic decision making and improving the stability of traffic light phases by combining flickers, waiting times, or vehicle queue sizes, as has been mentioned in [
53,
54,
55]. Works such as [
54,
56,
57], also confirm that these combinations have not yet been sufficiently addressed and suggest that despite the need to deal with scenarios with multiple intersections, problems with single intersections need to be solved by expanding their complexity scale. Recently, ref. [
56] mentioned that the use of stable phase mechanisms using variables such as flickers has not been fully explored. In summary, the use of DRL models and algorithms in simple intersections has open problems that still need to be addressed.
In this paper, we present a novel optimization method in which we involve three elements: vehicle queue size, flickers, and advantage actor-critic (A2C) RL with noise injection (NI), using a decentralized approach that takes traffic lights as individual agents, generating communication between the different traffic lights installed at a single intersection. This type of combination of variables, agents, and communication at a single intersection has not been used before and justifies exploring its performance.
The aim of this work is to develop and evaluate a decentralized DRL framework for traffic signal control at a single intersection, incorporating a novel adaptive reward function. Although focused on a single intersection, this study is highly relevant as it provides a foundational testbed for complex traffic control strategies, demonstrates the practical benefits of integrating multiple traffic factors, and establishes principles that can be extended to multi-intersection networks.
This work differs from existing approaches by focusing on traffic signal control at a single intersection using a decentralized DRL framework, demonstrating that even in a single-node scenario, decentralization enhances local adaptability. Unlike most studies, the proposed model integrates into the reward function traffic related variables, flickers, and queue length, together with A2C learning results, providing a more comprehensive assessment of traffic dynamics. The use of A2C improves learning stability and convergence compared to traditional DRL methods. In this way, each intersection operates as an independent agent adapting to local traffic conditions. In addition, the adaptive reward function optimizes key metrics such as queue lengths and traffic balance. Overall, this methodology enables autonomous and adaptive phase optimization, reduces congestion and delays, and is scalable to multi-intersection networks while maintaining decentralized control. Finally, by grounding the model in realistic traffic data and simulations, the approach offers practical applicability and a closer approximation to real-world traffic management, setting it apart from many theoretical or simplified studies.
The main contributions of the proposed study are summarized as follows:
- 1.
A decentralized DRL framework with NI for single-intersection ATSC in which each traffic light operates as an independent agent that adapts to local traffic conditions.
- 2.
A stability-oriented reward function that integrates queue length, flickers, and A2C learning feedback in an effort to mitigate premature phase changes and support smoother convergence.
- 3.
A comparative evaluation against seven baseline methods performed in the Simulation of Urban MObility (SUMO) platform using real traffic data from a Mexican city for calibration and validation, suggesting improvements in queue reduction and phase stability.
- 4.
An effort toward narrowing the gap between simulation-based ATSC research and potential real-world applications that emphasizes the role of stability-related variables in decentralized DRL settings.
The article is organized as follows: In
Section 2, a brief overview of ML and the techniques to be implemented will be given. The general problem formulation, as well as the details of the proposed model and algorithm, are presented in
Section 3. Simulation details and the results of the scenarios used to verify the effectiveness of the present model are presented in
Section 4. Next is
Section 5, where the analysis and discussion of the highlights of this research are established. Finally,
Section 6 presents the conclusions and future work on this line of research.
3. Materials and Methods
In this section, we formulate the ATSC problem as a DRL task, making a clear definition of all elements, such as scenario behavior, reward function, actions, and states. We present the functions used, such as experience replay (ER) and DQN, and explain the training with NI and DRL. The general architecture is illustrated in
Figure 1, where the model is named ATSC-DRLNI, while
Table 1 contains the notation used in this proposal.
3.1. System Description
The ATSC-DRLNI model is based on the joint implementation of techniques belonging to DRL and includes the CNN design, the data set (synthetic or real) processing, and the use of RL algorithms, in this case, ER and
-greedy policy. The general architecture is shown in
Figure 1 and will be explained below and in the following sections.
The DL scheme is divided into two streams, one where the inputs are processed by four CNN layers connected in series and another where the output of the third CNN is passed through a NI-layer, where GN is incorporated, whose output is added to the output of the fourth CNN. The NI-layer will improve the behavior of the network, specifically with regularization, robustness, and performance. This NI-layer implements a rectified linear unit function (ReLU) that generates a flow with a discrete probability distribution. The final output vector is used in (i) the reward function, (ii) to update the CNN weights with back-propagation at each step using the DQN algorithm, and (iii) to create the batches and buffers to be used for ER learning. Finally, the -greedy algorithm selects the actions.
In the selected DL architecture shown in
Figure 1, there is a bifurcation in
, the output tensor map of spatial features recovered in the third CNN. The first branch of this bifurcation is sent directly to the fourth CNN to further extract high-level spatial features and produce a new output tensor map,
. The other branch is directed to the NI layer, where, as explained before, random GN
is added to tensor
and then passed through a ReLU, which imposes a strict threshold (
) to eliminate weak negative activation signals that may be produced by the injected GN
. The output of the NI layer is the tensor
. Finally, the output tensors of the
and
layers in
Figure 1 are fused by direct sum,
, and then passed through three layers: Flatten, FC, and softmax in
Figure 1. The last layer,
, implements the policy
used in the A2C algorithm, and its output corresponds to the final result of the algorithm.
To stabilize the training process and ensure optimal convergence, the ATSC-DRLNI model includes an ER buffer and an -greedy action selection strategy with exponential decay. In the signal traffic control context, sequential traffic states are highly correlated, as the queue length at time t depends heavily on that at time . Feeding these highly correlated successive sequential states directly to the CNN induces high variance in the CNN output and instability in its behavior. To address this issue, the ER mechanism uses a finite-capacity buffer that stores agent experiences as transition tuples . At each learning step, mini-batches of tuples of uniform size are randomly sampled from buffer . This random sampling breaks the time correlation and allows the DQN algorithm to update network weights more stably.
As mentioned, action selection is based on an
-greedy strategy that allows us to obtain a trade-off between exploration and exploitation of the search space. This allows the agent to freely explore various phase synchronization combinations in the early stages of the learning and to exploit the learned Q values when convergence is near. The rate of exploration
decays exponentially with training episodes according to
where
e represents the current episode, and
is a constant that determines the speed of decay. The initial value of the exploration rate is
, which is aggressively reduced to reach a final value of
, which guarantees that the end agent depends largely on the optimized policy of the final episodes.
3.2. Actions
The set of feasible actions include all possible signals that a traffic light can adopt and, therefore, that an agent is free to choose from. For example, suppose that a traffic light change may occur within a given time frame T, and the agent starts a cycle with the green phase of the traffic light (), then, depending on the state of traffic, the agent will move to the yellow phase () and, finally, to the red phase of the traffic light (). To maintain a stable vehicular flow, after a time for , the agent should switch back to the to repeat the cycle, noting that only one phase can be active at any time. Action (, , ) of agent A at time t is denoted by .
3.3. States
The state at time
t, where an action is taken, is formed as a vector whose elements contain information from the environment, which is given by the specific features obtained from the traffic light sensors in use (length of vehicles, vehicle density, the distance between stopped and moving vehicles, etc). In our case, we use as information the total number of vehicles at a distance
D from the intersection under analysis and associate this number also with the actions of the traffic light signals, e.g.,
,
, and
and their respective time frames.
Figure 2 illustrates the data flow from states to Q-values.
3.4. Reward
The reward function is an essential component of the RL algorithm design, since it is the feedback index that evaluates the quality of the agent’s performance.
We implement a reward function at time
t,
, based on the combination of the vehicle queue, flickers, and the agent action
as follows:
where
is the probability of action
, decided in the A2C policy described below,
the size of the vehicle’s queue in the scenario considered, and
the number of flickers at time
t.
and
are appropriate factors to scale the variables involved.
This reward function has an additional penalty included when there are no vehicles and a flicker is produced, in that case,
with
the chosen penalty. The proposed reward then weighs the length of the queue and the number of flickers. A positive change in the reward indicates an improvement in the intersection condition, and conversely, a negative change in the reward shows deterioration. The reward function is used by the agents, in this case, the traffic lights involved in the scenario that will be introduced later on, and the interaction with the environment determines the policy of each agent. This reward function uses the DQN function presented before. To detect changes in the reward, the following time difference is introduced:
3.5. The Neural Network Structure
The structure of the proposed NN model is illustrated in
Figure 2. This NN is designed in such a way that it can process any state and produce a proper action. The input received comes from video cameras installed at several points before the intersection that, once processed, provide information about the number of vehicles at a certain distance
D of the intersection for the considered scenario, to be detailed further on. There are four CNN hidden layers aiming to maintain an adequate performance both in the NN and in the pre-processing. These layers include a NI-layer with a ReLU activation function. The number of output nodes for obtaining the Q-values functions is equivalent to the number of actions, which, in turn, are the triggers for obtaining the best reward. The NI-layer provides a statistical probability distribution by means of GN, which is added to the result of the last CNN. The output layer vector is the set of Q-values used to minimize the updating function
in Equation (
4). Algorithm 1 describes the A2C policy optimization in the ATSC-DRLNI model.
| Algorithm 1: ATSC-DRLNI policy optimization |
![Applsci 16 03833 i001 Applsci 16 03833 i001]() |
The policy is initialized with a random stochastic value to calculate the function . Then, given a state and an action carried out, the policy at time t, is determined. The reward time difference is computed in step 3 of the algorithm, where the goal is to adjust using , the current value of the reward, and the previous value . The term = in step 4 of the A2C algorithm represents the time difference error function, which serves as an estimator in the critic component of the algorithm. The function is essential for learning, as it evaluates the outcome based on the reward of the chosen action. When , it indicates that the probability of taking action At should be increased; conversely, if it is negative, the probability of taking action At should be decreased, because choosing it leads to poorer performance in the objective function.
Updating the critic will adjust the estimated value of using and , the learning ratio of the critic, not the actor. Finally, the new state must be set, and the algorithm is repeated from step 2.
5. Discussion and Limitations
Findings show a consistent positive correlation between the waiting time and the size of the queue length, similar to that shown in other studies [
53,
55], indicating that the inclusion of only one of two variables in the reward function is correct. The use of the number of flickers in the reward function showed a positive overall impact in the obtained results, in contrast to other methods for single intersections [
47,
48,
49,
53] where the reward function focuses only on waiting time and/or queue length without considering this variable.
The results presented suggest that optimization using the ATSC-DRLNI model can be a viable option to handle traffic lights and alleviate traffic congestion in real scenarios. From a theoretical point of view, results also align with those in [
53,
54,
55,
56,
57], as our simulation results indicate the convenience of using a combined reward function in single intersections.
There is research that has also used flickers [
53,
55] in a DRL context with multi-objective models, showing reductions up to 18% in waiting time. However, these studies do not combine queue length and flickers in the reward function.
The good performance of the ATSC-DRLNI model in balancing traffic (
Figure 9) and in queue reduction (
Figure 6) are a direct consequence of the NI layer, which, by introducing controlled disturbances during training, forces agents to discriminate between spurious fluctuations in demand and real tendencies in congestion. This, in turn, prevents “over-reactions” in the control policy to small queue increments, a behavior that in other models (such as standard DQN) produces unstable phase changes. System stability, as shown in
Figure 10, corroborates that agents have learned a more robust control policy that avoids overfitting with the data training set.
Although the ATSC-DRLNI framework does not explicitly implement a formal multi-objective optimization scheme, the correlation analysis across global, off-peak, and peak regimes indicates that stability-related and efficiency-related objectives do not exhibit structural conflict within the learned policy. The weak correlations between flickers and congestion metrics, together with the strong and consistent relationships among efficiency indicators, suggest that penalizing flickers does not compromise operational performance.
Nevertheless, an explicit multi-objective reinforcement learning (MORL) formulation could be explored in future work to formally characterize potential objective interactions under more heterogeneous traffic conditions or expanded state representations.
Beyond this conceptual consideration, the ATSC-DRLNI model presents several practical limitations. First, simulation times are longer compared to the other benchmark models evaluated. Second, certain environmental factors—such as pedestrians, priority vehicles (e.g., ambulances or police cars), and autonomous vehicles—were not included due to data and modeling constraints. Third, the current evaluation focuses on a single intersection, and more complex multi-intersection scenarios remain to be analyzed.
Future research should therefore address large-scale urban networks, modeling each intersection as a decentralized agent within a multi-agent deep reinforcement learning (MADRL) framework [
78,
79]. In addition, field testing will be necessary to assess the real-world applicability and robustness of the proposed ATSC strategy [
31,
47,
78].
6. Conclusions
This research investigates the application of DRL to optimize ATSC and emphasizes the trade-off between minimizing queue lengths and suppressing signal instability at complex intersections. We developed and simulated a training environment on the SUMO platform, allowing the proposed ATSC-DRLNI model to learn signal timing policies through an A2C framework. Experimental results suggest that the agent skillfully balances queue size and phase flickers, outperforming seven benchmarks—including multi-agent approaches such as MADRL and MARDDPG—with a 40% reduction in queue length and sustained stability. However, although these results highlight the considerable potential of decentralized traffic management, they are limited to the simulated contexts described here.
A key contribution of this study is the analysis of how the A2C algorithm improves communication between agents and learning stability, enabling simultaneous optimization of queue lengths and signal flashes under congested traffic conditions. However, the disparity between the optimizations derived from simulation and practical implementation remains a major obstacle, especially with regard to physical constraints and unmodeled stochastic elements. To address this disparity, future research focused on validating these control strategies in increasingly realistic simulations or hardware-in-the-loop (HIL) is needed.
In addition, the methodology proposed in this paper could bridge the gap between theoretical autonomous traffic systems and their practical implementation, although it requires rigorous safety evaluations before real-world deployment. The proposed reward structure enables a balanced integration of efficiency-related metrics (AQL, AWT, ATT) and flickers, achieving consistent performance across off-peak and peak traffic regimen. Although DRL is widely studied in traffic control, translating these models into real-world settings remains challenging due to data constraints, safety requirements, and operational complexity. By grounding both training and validation in empirical traffic data, this framework contributes to narrowing the gap between simulation-based advances and practical implementation. Future work will explore explicit multi-objective reward formulations, the incorporation of vulnerable road users and emergency vehicles into the state representation, and extensions toward multi-intersection settings. Overall, these findings reinforce the practical potential of DRL as a scalable strategy for advancing adaptive traffic control systems (ATCSs) toward real-world deployment.