Hybrid Model-Based Traffic Network Control Using Population Games

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Title: Population Games-Based Control Strategies for Urban Traffic Systems

This study (asi-3741624) proposes an urban traffic control approach based on population game theory. By modeling the traffic network as a hybrid system combining continuous vehicle storage dynamics with discrete traffic signal switching the researchers developed five control strategies, including adaptive methods such as Smith dynamics and replicator dynamics, as well as a virtual game-based fixed-time strategy. A VISSIM-MATLAB co-simulation platform was established to evaluate the performance of these strategies within an eight-intersection network. My comments are to help improve the paper further.

1. The equations in Section 2, Mathematical Description of an Urban Traffic Network, are not numbered, and the symbols used in the equations throughout the paper lack a unified explanation. It is recommended that all equations be properly numbered and a comprehensive list of notations be provided to ensure clarity and consistency.
2. The description of the DAE system's mode switching in Equation (6) is not sufficiently precise. In the paper, mode switching is handled merely through a simple threshold-based rule. The authors are advised to adopt a more rational and sophisticated approach for determining threshold conditions to enhance the accuracy of the switching mechanism.
3. In Section 5.2 Population Dynamics, the description is overly brief. The authors should provide a more detailed and thorough explanation of this part to enhance the readers’ understanding of the underlying mechanisms and their relevance to the proposed control strategies.
4. In Section 6, the authors should supplement the technical details of the COM interface and clearly specify the object mapping relationship between MATLAB and VISSIM to enhance the reproducibility and clarity of the co-simulation framework.
5. In Section 8, where the five different scenarios are compared, the methodology of comparison is not clearly described. For instance, it is mentioned that the replicator dynamic outperforms the Smith dynamic in terms of TTV, but the specific data—such as the exact values or the percentage improvement—is missing. The authors should present concrete numerical results to support these comparisons and make the performance differences more transparent and convincing.

 

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript investigates population games-based control strategies for urban traffic systems, aiming to mitigate congestion by optimizing traffic signal green times. The manuscript is intersting but I have some comments.

1. The novelty of hybrid system modeling is not clear. The manuscript claims "hybrid system modeling" as an innovation but fails to explicitly distinguish it from existing game theory-based traffic control models.
2. The rationale for fitness functions (e.g., Smith dynamics relying on queue length-green time ratios) and fictitious play’s payoff function (cumulative queue length) lacks empirical validation. 
3. he traffic flow values in Table 2 (e.g., 2400 veh/h for horizontal links in Scenario 3) are not supported by references to real-world data.
4. The discussion attributes the superiority of Smith and replicator dynamics to "decentralized characteristics" but does not elaborate on how their decision mechanisms adapt to traffic volatility. 
5. When introducing adaptive strategies, citations to game theory studies (e.g., [18,20]) do not address limitations of existing methods in handling saturated or variable flows

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for the opportunity to review your manuscript titled "Population Games-Based Control Strategies for Urban Traffic Systems." While the topic is clearly relevant and timely, and the expertise of the authors is evident, I have somewhat mixed impressions about the manuscript. On the one hand, it demonstrates thoughtful effort and technical understanding; on the other, it lacks development in several key areas that significantly impact its clarity and contribution.

The title is too general, be more specific. The abstract are appropriate, but if you decide to enhance the content, the abstract will also need to be updated accordingly. The literature review is deep and focused, showing a solid grasp of existing work. However, the scope is overly concentrated on this specific niche, which makes it difficult to assess whether the novelty of the proposed approach truly exceeds what is already explored in the broader literature. Including a summary table that compares related work—indicating who did what and how your contribution differs—would make the novelty clearer and much easier to assess.

Section 2 is good chapter, you did a great work with it. It describes the core problem in a clear and accessible way. The two defined parameters in the model are simple yet meaningful, providing a solid basis for measurement and comparison. However, I found the connection to game theory in this model lacking. The theoretical integration of game theory is introduced too briefly, and its role is not clearly developed or justified.

The description of the applied methods is overly superficial. A clearer presentation of the individual methods—especially how they differ from one another and where they are commonly applied—would significantly strengthen this section. Currently, the explanations feel too light and introductory.

The case study is relatively weak.A more life-like dataset or a more natural/imblanced intersection system will show more difference. The table is hard to interpret on its own and requires both visual aids (such as graphs) and narrative explanations to make the results meaningful. This analysis would benefit from being presented in a dedicated section, not scattered across brief sections and the conclusion.

Speaking of the conclusion, it would be better suited for a true summary of key findings and broader reflections. At minimum, it should address theoretical limitations, application-specific constraints, what was not considered or tested, the potential for real-world implementation, and directions for future work. Currently, this reflection is missing.

The grammar, text and formating are consistent and acceptable, but the too many chapters are not good for clarity and structure.

Additional technical remarks:

• In Section 2, the mathematical equations are not consistently closed with an (x) mark.
• The reference list at the end is inconsistently formatted, with some missing DOIs and several citation style issues. This should be reviewed and corrected to meet the journal’s standards.

In conclusion, the paper presents a valuable idea, but several aspects are underdeveloped, including the theoretical formulation, methodological clarity, and experimental communication. I therefore recommend a major revision before the manuscript can be considered for publication.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The research background of this article is that modern traffic management needs to address the increasingly complex challenges of urban road networks. In response to the poor performance of traditional methods in alleviating congestion and optimizing traffic flow, a group game control strategy combining hybrid systems and graph theory is proposed. Through the use of VISSIM and MATLAB software simulators, multiple traffic control strategies based on group dynamics and payoff functions are implemented and compared, including Fictious Play (based on a fixed time perspective) and adaptive strategies, such as Smith, Replicator, Logit, and Brown Von Neumann Nash (BNN), to compare the performance of offline and adaptive control methods under different conditions. Although I am not an expert in this field, I think this is quite an interesting research. However, to publish it on the journal I also have some question to discuss with authors.

 

1. The paper mentioned that the research mothed combined with hybrid systems and graph theory. Is there a similar attempt in existing literature to explore the control strategies for urban traffic systems? In fact, although I am not an expert in this field, my biggest doubt is about innovation. I think it is necessary for the authors to clearly state their specific contributions to traffic control theory or practice in the paper.
2. Secondly, regarding the selection criteria for dynamic models, I would like to ask why Smith and Repligator dynamics were chosen as the main comparison objects? Do they have theoretical support for their adaptability in traffic scenarios compared to other dynamics such as Logit or BNN?
3. In terms of specific technology, how do the authors handle continuous dynamics (such as changes in traffic flow) and discrete events (such as traffic light switching) in traffic signal control? Is there a formal model description? The cost function is a key factor affecting the convergence and efficiency of group games. How does the author define the profit function? Have you considered the mutual influence between different vehicle path choices?
4. Are the five selected traffic scenarios diverse enough? Has it covered typical scenarios such as urban main roads, densely populated intersections, and low-density areas? How are the parameters in the control strategy, such as learning rate and profit weight, optimized through the coupling of VISSIM and MATLAB? Has the sensitivity of parameters been analyzed?
5. The author mentioned multiple indicators such as parking frequency and average speed, but has the relationship between these indicators been thoroughly analyzed? For example, does reducing the number of parking times necessarily lead to a decrease in total travel time? Why do Smith and Replicant dynamics perform better at high saturation? Is there a specific mechanism that causes this phenomenon? Is there a theoretical explanation? In fact, the analysis and explanation of the model conclusions in this paper are not comprehensive enough.
6. The current research is a simulation conducted on small or medium-sized transportation networks. Is this method applicable to larger scale urban transportation networks? Will computational complexity become a bottleneck? Does the system have real-time response capability? How long does the entire feedback process from queue length collection to green light time adjustment take? Does it meet the actual control requirements?

Author Response

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Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

The paper explored different game theory-based control strategies in an 8-intersections traffic network modeled by means of hybrid systems and graph theory, using a software simulator that combines the multi-modal traffic simulation software VISSIM and MATLAB to integrate traffic network parameters and population game criteria.However, there are the following problems with this paper that need to be modified
1) The paper selects a fixed time signaling scheme by means of fictitious play dynamic, and adaptive schemes, for the hybrid urban traffic system, which is based on a fictitious game dynamics and adaptive schemes, is suitable for verifying the proposed method.
2) For the traffic network model, the paper lists different dynamic models, Population Dynamics and Replicator Dynamics. In the simulation process, which dynamic model is selected and what are the differences between these models?
3) Brown-von Neumann-Nash is a typical game theory-based control. Its advantages and disadvantages are discussed in such traffic networks.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thanks for the authors' revision. The paper was improved a lot. 
I ensured that the authors addressed the concerns raised appropriately and improved the paper. I am satisfied with the current version and would like to recommend it to be accepted for publication.

Reviewer 2 Report

Comments and Suggestions for Authors

The revision is fine

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for the thoughtful revisions and the clarifying explanations you provided regarding the previously unclear steps and modeling choices. I appreciate the additions and clarifications, which have helped to make the manuscript more transparent and coherent. From what I can see, you have successfully addressed not only my comments but also those raised by the other reviewers. These improvements have clearly raised the overall quality of the paper. With these revisions, I am happy to recommend the manuscript for acceptance.

Reviewer 4 Report

Comments and Suggestions for Authors

I appreciate the author's hard working and I think now it could be published on the journal.