Optimal Placement of Sensors in Traffic Networks Using Global Search Optimization Techniques Oriented towards Traffic Flow Estimation and Pollutant Emission Evaluation

Round 1

Reviewer 1 Report

The content is interesting. However, these comments to improve the paper, please consider it.

Please, rewrite the abstract again, it has a lot of problems. For example:

- In sentence 2, consider specifying the types of analyses involved in traffic flow estimation (e.g., statistical analysis, mathematical modeling). 

- In sentence 4, instead of "hardware constraints," you might want to specify what these constraints entail (e.g., limited power supply, processing capabilities). 

- In sentence 6, you could clarify what constitutes an "optimal array" of physical sensors. Are there specific criteria for optimality? 

- In sentence 8, consider briefly mentioning the significance of achieving full link flow observability for traffic systems.

- In sentence 10, specifying why maintaining the structural observability of the entire traffic network is important would provide additional context.

- In sentence 12, you might want to briefly explain what a "Luenberger observer" is, especially for readers who may not be familiar with the term.

- In sentence 15, providing a brief overview of the key findings of the numerical simulations could enhance the reader's understanding.

Clarify the transition between the introduction and the specific focus of your paper. You introduce the concept of smart cities and sensor technologies but then dive into the sensor selection problem without a clear connection. Perhaps explicitly state that your paper addresses one of the critical challenges in implementing smart city technologies, which is strategically selecting sensors for traffic flow estimation and pollutant emission evaluation.

- Consider breaking down some lengthy sentences for improved readability and clarity. For example, in sentences 23-29, you could split the information into two or more sentences to avoid overwhelming the reader with too much information at once.

- Provide a brief overview or definition of observability metrics (rank, trace, condition number of the observability Gramian) mentioned in sentences 68-69, especially for readers who may not be familiar with these terms.

- Sentence 76 could be clearer. It might be helpful to specify the urban area of interest or provide a general context for the traffic model you're discussing.

- Ensure consistency in referencing previous works. For instance, you mention "[26]'s work" in sentence 67, but it's not clear what this reference is without the citation. Make sure it's clear which work you're referring to.

- Consider providing a brief explanation or rationale for choosing simulated annealing (SA) heuristic for sensor selection in sentence 78. Why was SA chosen over other optimization methods?

- In sentence 84, clarify what is meant by "exhaust search procedure." It's not a commonly used term, so providing a brief explanation or context would be helpful.

- Ensure clarity in Section 7 about the simulations conducted and the specific findings presented. What case study is being referenced, and what are the main results obtained from it?

- Also, I recommend you use: First, second, and so on, instead of a point list, on lines 144 and after. You are using the point lists too much.

- Please explain the Figure labels and Table labels very well.

- No need to define the algorithms like generic methods. Please explain why you used the method in your research.

- On page 12, remove A, and B data. It is not necessary.

- Remove Tables 1 and 2, it is not necessary. Figure 6 too. Figures 12, 13, and 14 are not understandable.

- The conclusion is too short and not enough.

Author Response

Plese refer to the Section "Answers to Reviewer 1" reported in the attached document.

Thank you.

Author Response File: Author Response.pdf

Reviewer 2 Report

1 Punctuation mark should not be added to the end of the article title. So the full stop must be deleted

2 Some academic terms are bewildering, e.g. “overseeing expansive systems” and “structural observability”. It is better to give more detailed explanation targeting the purpose of the related research.

3 LTI state equations were used to represent the traffic system, however, a real transportation network is dynamic and nonlinear. What are the discrepancies between the practical system and theoretical model? The influence of the differences on estimation must be analysed and considered as well as comparing the adopted method with classic traffic models.

4 In computer simulation, why are all inputs discrete values? Traffic flows such as vehicle speed are continuously changing along with unpredictable accidents on roads.

5 Regarding the pollutant emission evaluation, exhaustive gases generated by vehicles are obviously different when considering the size, weight and engines while the mathematical model didn’t consider the differences? Additionally, hybrid and electric-powered vehicles are becoming popular, it is necessary to address these considerations while building the model.   

Writing quality is fine except for some grammar errors

Author Response

Plese refer to the Section "Answers to Reviewer 2" reported in the attached document.

Thank you.

Author Response File: Author Response.pdf

Reviewer 3 Report

This paper proposed an approach to find the minimal set of sensors with effective Observability and state reconstruction performance to address the sensor selection problem for traffic monitoring in road network systems. Using a compartmental network traffic model, the problem is transformed into a mixed-integer non-linear programming problem. Simulated annealing is employed to find the global minimizer. Numerical simulations validate the approach, comparing with heuristics based on genetic algorithms and exhaustive searches. Performance analysis using a digital twin of a transport network has been carried out to assess traffic flow and associated pollutant emissions.

Overall, this paper is interesting and well written. However, several areas could benefit from further clarification.

- Since some paper contents have already been published, it would be beneficial to specify the contribution of this paper.

- It would be beneficial to include a table containing the notations to help readers to reference and understand the mathematical framework.

- There is an inconsistency of the notation x_i(t).

Line 181: x_i(t) represents the number of vehicles in the i-th compartment.

Line 187: x_i(t) denotes the traffic flow (vehicles per unit time) in the i-th road sector

- Equation (13) and Line 264 utilize the index i ranging from i, . . . , n. It is recommended to define this range, i = 1, …, n, for clarity.

- There is no performance comparison of the proposed approach to other related works in the field.

Author Response

Plese refer to the Section "Answers to Reviewer 3" reported in the attached document.

Thank you.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

All concerns have been addressed.

Language quality is OK except for minor grammar mistakes.

Author Response

We have thoroughly reviewed the paper to correct any grammatical errors.

We appreciate your assistance in the review process.

Reviewer 3 Report

The authors have incorporated my suggestions to refine the paper and addressed my concerns. I find the revised version is fine and have no further questions.

Author Response

We appreciate your assistance in the review process.