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Research on Urban Road Traffic Network Pinning Control Based on Feedback Control

Sustainability 2023, 15(12), 9631; https://doi.org/10.3390/su15129631

by Guimin Gong, Wenhong Lv^* and Qi Wang

Reviewer 1:

Salvador Martinez Puche

Reviewer 2:

Marek Ogryzek

Reviewer 3: Anonymous

Reviewer 4: Anonymous

Sustainability 2023, 15(12), 9631; https://doi.org/10.3390/su15129631

Submission received: 18 May 2023 / Revised: 10 June 2023 / Accepted: 12 June 2023 / Published: 15 June 2023

Round 1

Reviewer 1 Report

The research is considered as the simulation and applied verification of a traffic regulation model based on fixation control, based on the proposals extracted from the background literature review

However, the methodology is confusing, since the object of study is not determined until well advanced in the writing of the work, epigraph 4, which is identified with Xin'an street, Huangdao district in the city of Qingdao. Beyond the verification of the use of the control system, the objectives are not very explicit and systematic, despite the fact that the mathematical formulas used to determine the quantitative results are described in several figures.
Although these formulas are applied to real data from the selected road to confirm the benefits of an adequate implementation of the control model with the possible corrections to take into account, table 1 alludes to a survey. But the process of obtaining these data is not made explicit. It would be advisable to conveniently organize that information.
Lastly, the conclusions are too concise, without going into an analysis of other factors or parameters that would be of interest and that are mentioned obliquely in the introductory part of the research on automated vehicle driving. Likewise, it does not investigate how the use of new technologies with digitized driving systems connected to traffic lights or other traffic regulation equipment, for example, can influence.

Author Response

Point 1

However, the methodology is confusing, since the object of study is not determined until well advanced in the writing of the work, epigraph 4, which is identified with Xin'an street, Huangdao district in the city of Qingdao

Response 1:

Thanks for your comments and suggestions. Regarding your question, our explanation is as follows.

The research idea of this paper is as follows: firstly, the state equation of the urban road traffic network is constructed, then a drafting control model for the operation state of the road network is built on the basis of the state equation, and finally the simulation of the proposed drafting control scheme is carried out to verify the effect of the model by using the sub-region of Xin'an street as a case.

Point 2:

Beyond the verification of the use of the control system, the objectives are not very explicit and systematic, despite the fact that the mathematical formulas used to determine the quantitative results are described in several figures

Response 2:

Thanks for your comments and suggestions. According to your suggestion, we have included a detailed description of the purpose of this paper in section1, which specifies the objectives of this paper.

1.Introduction

………….

The main work of this paper proposes a pinning control scheme considering feedback, by changing the green letter ratio of each phase at key intersections and achieving the purpose of changing the flow rate of each road section according to the correlation between key intersections and each road section, so that the road network as a whole reaches a new stable state. The traffic congestion is relieved with a smaller control cost and the operational efficiency of the road network is improved.

The specific work is as follows:

(1) The state equation of urban road traffic network is constructed considering the mobility of traffic flow, and the correlation model between road section flow and key intersections in the road network is established by introducing parameters such as saturation flow rate, correlation degree and turning ratio

(2) A pinning control strategy is proposed to reduce the flow of congested road sections in the road network by judging the operation status of traffic flow in each section of the road network and adjusting the signal timing of key intersections so that all sections are in a smooth flow

(3) Simulation of the pinning control strategy and method is carried out on the regional road network of Xin'an Street, and the results show that the proposed strategy can effectively reduce the delay and queuing time in the road network.

Please see the Section 1 in the revised manuscript.

Point 3:

Although these formulas are applied to real data from the selected road to confirm the benefits of an adequate implementation of the control model with the possible corrections to take into account, table 1 alludes to a survey. But the process of obtaining these data is not made explicit. It would be advisable to conveniently organize that information.

Response 3:

Thanks for your comments and suggestions. According to your suggestion we describe the data sources in detail in Section 4

4.Simulation analysis

……..

After the simulation area was determined, the traffic signal phases and timing of each intersection in the area were first investigated using the manual survey method. At the same time, the traffic volume on each road section at a certain time of the weekday evening peak was investigated using the floating vehicle method with ordinary cabs as the test vehicles.

Please see the Section 4 in the revised manuscript.

Point 4:

Lastly, the conclusions are too concise, without going into an analysis of other factors or parameters that would be of interest and that are mentioned obliquely in the introductory part of the research on automated vehicle driving. Likewise, it does not investigate how the use of new technologies with digitized driving systems connected to traffic lights or other traffic regulation equipment, for example, can influence

Response 4:

Thanks for your comments and suggestions. According to your suggestion，we conclude with an analysis of the parameters in the implicative control model, along with a description of the shortcomings of this paper and an outlook for future research.

Conclusion

In this paper, an urban road network pinning control method for critical intersections is designed by combining the characteristics of road networks. Firstly, an urban road network traction control model is established based on the general complex dynamic network state equation and its traction control model. The model considers the coupling relationship between intersections and road segments to establish, and introduces the degree of coupling and turning ratio to describe the interaction of traffic between key intersections and road segments. The degree of association is the reciprocal of the number of road sections between the road section and the key intersection and whether the traffic flowing through the key intersection flows into and out of the road section as the coupling between the road section and the key intersection, and the turning ratio is the product of the turning ratio of all intersections out of the shortest path when the traffic flows from the key intersection into and out of the road section. The parameter takes into account the control effect of key intersections on road sections will decrease with the growth of distance, and further proves that the road sections directly connected with key intersections should be the focus of monitoring in the paper.

The actual flow rate on each road segment is optimized to be close to the desired flow rate by applying drafting control to the critical intersection and adjusting its signal timing, where the closer the road segment is to the critical intersection. With the objective of minimizing the squared difference between the actual flow and the desired flow on each road section, the most appropriate signal timing is derived by satisfying the constraints of minimum and maximum green time for each phase and the flow on each road section is less than the congestion threshold. At the same time, 1.5 times of the desired flow rate is taken as the threshold value, and when the traffic volume of a road section reaches this threshold value, feedback is required for a new round of signal timing adjustment of the key intersection drafting control scheme. Finally, the simulation analysis combined with the actual road network shows that the proposed drafting control scheme reduces the average delay time and the average stopping time of the road network by 35.03s and 18.37s, respectively, compared with the original control scheme, and the congestion of the road sections directly connected to the critical intersections is greatly improved. To a certain extent, the congestion of the road network is alleviated and the operational efficiency of the road network is improved.

However, the method proposed in this paper has many shortcomings, and further improvements can be made in future studies. In this paper, only one key node is selected to control the control area, and the scale of the road network and the number of control nodes are not studied. Since the simulation area selected in this paper is a very small area of the road network, the control method is relatively feasible, and the number of control nodes selected and the control effect need to be further studied when the road network area is expanded. In addition, with the advancement of intelligent transportation and driverless technology, the information between vehicles and traffic control devices will be interoperable, and the traffic signals and traffic control devices in the road network area can be considered for advance planning based on the travel information of vehicles in the future to fundamentally alleviate the traffic congestion.

Please see the Section 5 in the revised manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

First of all, I would like to say that this manuscript focuses on a very interesting research problem.

TITLE

The article’s title is suitable with the content of the paper.

ABSTRACT

The abstract is well-designed and briefly express the present research thus being of interests and readable thus capturing the reader’s attention. It present in an appropriate manner the main research hypothesis, the problem statement, the methods and the main findings.

KEY WORDS

The key words are appropriate to the present research and are clearly stated.

THE PAPER S STRUCTURE

The structure of the paper is correct in line with the journal standards and meet the publication requirements considering the paper logic but the paper should be organized into the following sections: 1) Introduction; 2) Research methods; 3) Study area; 4) Results and Discussion; 5) Conclusion.

THE METHODS

The methodological design is appropriate and the methods fit well to the present investigation. The methods used in the study are well expressed both in the graphical form as well as in the main text of the manuscript.

The process of the research must be described carefully – maybe You could use a graph?

THE MAIN ANALYSIS

The main research is well design and appropriate conducted.

CONCLUSIONS

The conclusions fit well summarising the main ideas of the present analysis.

THE GRAPHICAL SUPPORT

The graphical support is well formatted, appropriate illustrating the text content.

THE ENGLISH LANGUAGE

I think the English is ok as far as I could see. I enjoyed to read this paper in English and the language seems well but I think that an opinion of a native English speaker is welcomed. In other words, if the authors used a specialised proofreading services and they could prove this aspect I trust the opinion and the work of this proofread service. On the other hand, I put my trust regarding the English language on the journal editors but I repeat the language seems well.

RECOMMENDATIONS

I recommend the publication of this paper with some minor revision considering the above mentioned aspects:

1. The purpose of the work needs to be more clearly stated. Describe the purpose of the work, although the reader should guess but these are the trends.

2. Describe the research area in detail. Refer to the research carried out in this area.

3. Make a critical evaluation of your method, describe the problems in its implementation, limitations of use, cost and time consumption, etc.

4. You don't need to do the literature review as a separate chapter because the description of the method is quite long but the number of articles cited is too small.

Focus on Western literature and the solutions found there.

A few examples of omitted aspects:

· sustainable transport

Greene, D.L.; Wegener, M. Sustainable transport. J. Transp. Geogr. 1997, 5, 177–190, doi:10.1016/s0966-6923(97)00013-6.

Richardson, B.C. Sustainable transport: Analysis frameworks. J. Transp. Geogr. 2005, 13, 29–39, doi:10.1016/j.jtrangeo.2004.11.005.

· legal aspects (there are infrastructure networks in the roads and by the roads, which causes restrictions because the law applies not only to what is on the road, but also under and over the road)

· Ogryzek M, Klimach M., Niekurzak D., Pietkiewicz M., Using Cartographic Documents to Provide Geoinformation on the Rights to Real Estate – Taking Poland as an Example, International Journal of Geo-Information, 2019, Volume 8(12), s.1-15, 530; doi: 10.3390/ijgi8120530

· Calculation of roads for car traffic at the expense of bicycle paths and pedestrian paths and, in turn, the system of bypasses

· Torslov N. Traffic in Copenhagen 2009,; Copenhagen Traffic Department, 2010: Copenhagen, 2010;

· Positive impact of new technologies and transport systems

Goldman, T.; Gorham, R. Zrównoważony transport miejski: cztery innowacyjne kierunki. Techno. soc. 2006 , 28 , 261–273.

· artificial intelligence in transport

Abduljabbar, R., Dia, H., Liyanage, S., & Bagloee, S. A. (2019). Applications of artificial intelligence in transport: An overview. Sustainability, 11(1), 189.

Miles, J. C., & Walker, A. J. (2006, September). The potential application of artificial intelligence in transport. In IEE Proceedings-Intelligent Transport Systems (Vol. 153, No. 3, pp. 183-198). IET Digital Library.

· Transportation demand management (TDM)

Ferguson, E. (1990). Planowanie, rozwój i wdrażanie zarządzania popytem na transport. Journal of American Planning Association , 56 (4), 442-456.

I want to see the revised version of this paper before publication for a final acceptance and to ensure that the revision has been completely and carefully made.

Author Response

Point 1：

The purpose of the work needs to be more clearly stated. Describe the purpose of the work, although the reader should guess but these are the trends：

Response 1:

Thanks for your comments and suggestions. According to your suggestion, we have included a detailed description of the purpose of this paper in section1, which specifies the objectives of this paper.

1.Introduction

………

The specific work is as follows:

Please see the Section 1 in the revised manuscript.

Point 2：

Describe the research area in detail. Refer to the research carried out in this area：

Response 2:

Thanks for your comments and suggestions. According to your suggestion, we have reorganized the introductory section.

Please see the Section 1 in the revised manuscript.

Point 3：

Make a critical evaluation of your method, describe the problems in its implementation, limitations of use, cost and time consumption, etc.

Response 3:

Thanks for your comments and suggestions. According to your suggestion, we critically evaluate this paper in the conclusion section and also provide an outlook on the next research directions

Conclusion

……

Please see the Section 5 in the revised manuscript.

Point 4：

You don't need to do the literature review as a separate chapter because the description of the method is quite long but the number of articles cited is too small.

Response 4:

Thanks for your comments and suggestions. According to your suggestion, we have redescribed the introductory section, added missing aspects, and reduced the description of the literature methods.

1.Introduction

The significant growth in the number of motor vehicles worldwide has led to an increasing demand for travel, and the urban road network needs to be expanded in order to meet the travel demand. However, considering the limitation of land, it is un-realistic to build roads without limitation. In order to meet the travel demand of motor vehicles, many scholars have conducted research on sustainable development of transportation[1-2], transportation infrastructure[3-4], new technologies [5], artificial intelligence [6-7], and transportation demand management [8]. However, considering the restrictive situation in terms of land use, laws and regulations, traffic safety issues and traffic congestion are still urgent challenges in many countries.

The research of existing traffic control methods has risen from single point control and arterial control to area control. SCOOT [9] and SCATS [10] are the first adaptive control systems proposed, however, the SCATS system does not use traffic models, which limits the optimization process of signal timing and does not fit well with the dynamic traffic flow characteristics, while SCOOT uses accurate mathematical models to determine the appropriate control strategy, which leads to long simulation This leads to a long simulation time, which creates a conflict between real-time and relia-bility.

Subsequent scholars have studied the control methods of road traffic networks from different perspectives. Traffic response urban control is a more typical basis for developing traffic signal control strategies. Febbraro [11]、Chiou [12] et al. proposed an optimal control scheme for traffic signals based on traffic response demand as a way to reduce vehicle queue length and improve the toughness of urban road networks. On the basis some scholars started to improve the research on TUC methods. Dino [13] and Manolis [14] introduced a quadratic planning approach and a local drive-based approach for hybrid studies with TCU, respectively. Kouvelas et al. [15]propose a hy-brid signal control strategy that integrates TUC and DB strategies, since the DB method is only applicable to unsaturated traffic conditions and the TUC method is applicable to saturated traffic conditions, the paper mixes the two methods to improve the con-trol of the network

Godfrey [16] first proposed the role of macro fundamental maps in traffic net-work analysis. In recent years, Ekbatani [17], Aboudolas [18], Zhang [19] and Knoop [20] et al. have conducted extensive studies on traffic networks using MFD theory. Yang et al [21] proposed a fuzzy RBF neural network PID-based regional boundary control method for traffic networks. Li et al [22] proposed a traffic flow transfer model considering MFD constraints and investigated its relationship with network traffic at-tributes. Wang et al [23] proposed a multi-region achieving consistent state feedback without considering the differences in congestion conditions and equilibrium in each sub-region control method. Li et al [24] proposed a model-free adaptive control strat-egy for urban road traffic networks based on dynamic linearization techniques and predictive control, considering perimeter control. Based on regional traffic control, Liu et al [25] combined macroscopic fundamental graph theory with perimeter and boundary flow control methods to achieve a combined strategy of traction control and active control.

Meanwhile, with the development of intelligent transportation, more and more advanced machine learning techniques are being applied to regional traffic control methods [26-27].

However, most of the existing control methods consider control efficiency, few consider control cost and further consider control cost in combination with control ef-ficiency. Therefore, this paper studies an urban road traffic network control method based on traction control from this perspective. The basic idea of pinning control is to suppress the spatiotemporal chaotic behavior of the whole network by applying con-stant input control to some nodes in the network [28]. In 2002, Wang et al. [29]first in-troduced the pinning control into the synchronization control of scale-free dynamic networks, and the research results showed that the whole network can reach the syn-chronization state after applying control to some nodes in the network. The urban road also has typical small world effect and scale-free effect, so this paper introduces pin-ning control for the study.

Please see the Section 1 and References in the revised manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

This study proposes a pinning control strategy for urban road networks, optimizing signal timings at key intersections to minimize congestion and improve traffic flow efficiency. The manuscript needs improvements before it can be recommended for publication. Please see below further comments for consideration:

- The Abstract lacks an introduction to the topic that would encourage potential readers. In addition, the reviewer recommends adding numerical results.

- The Introduction requires a more in-depth review of the literature supporting some of the statements.

- The framework of the overall procedure is not quite highlighted in the Introduction. It is suggested to delete the final paragraph of the Introduction; a graphical abstract could cover (or include) this paragraph.

- Figures, Equations, and Tables are not always recalled in the text (e.g., Figure 4, Table 1, Equation 1, etc.). In addition, they should be placed close to the text where they are discussed.

- Figure 1 please add a legend.

- Please check the Figure/Table numbering (i.e., Lines 107, 308, 323, and 372).

- Section 3.1: please check and update the manuscript according to the Journal template.

- The reviewer suggests improving the quality and readability of Figures 5 and 6.

- Lines 359-362: it is not clear the use of Python and Vissim.

- The Conclusions section lacks in terms of numerical results.

The writing quality of this manuscript is below the standard for journal articles. The structures of sentences and paragraphs are not clear, and there are many grammatical and typographical errors.

Author Response

Point 1：

The Abstract lacks an introduction to the topic that would encourage potential readers. In addition, the reviewer recommends adding numerical results

Response 1:

Thanks for your comments and suggestions. According to your suggestion, we have added a description of the paper topic and numerical results to the abstract.

Abstract

The development and application of pinning control methods create conditions for traffic area control, and the purpose of global control of road network is achieved by controlling a small number of intersections in the road network. Based on this, an urban road network pinning control strategy is designed in this paper. Firstly, this paper establishes the state equation of urban road traffic network according to the characteristics of traffic flow, and proposes an associated state equation of road sections and key intersections. Secondly, by adjusting the signal timing scheme of key intersections as the target of pinning control, it can restrain the road network to achieve the state with the minimum difference between the actual flow and the desired flow on each road section. At the same time, considering the dynamic nature of traffic flow, the flow rate on the road section will change continuously, so a feedback control mechanism is established to determine the threshold value for each road section to enter the congestion state, and when the flow rate of a road section exceeds its threshold value to reach the congestion state, the signal timing scheme of the key intersection needs to be adjusted again to ensure that the flow rate on the road section is always lower than its threshold value to enter the congestion state. The results show that the average delay time and average stopping time of the road network are reduced by 35.03s and 18.37s, respectively, compared with the original control scheme, proving that the control strategy can effectively reduce congestion and improve the operational efficiency of the road network.

Point 2

The Introduction requires a more in-depth review of the literature supporting some of the statements

Response 2:

Thanks for your comments and suggestions. According to your suggestion, we have reorganized the introductory section.

Please see the Section 1 in the revised manuscript.

Point 3

The framework of the overall procedure is not quite highlighted in the Introduction. It is suggested to delete the final paragraph of the Introduction; a graphical abstract could cover (or include) this paragraph

Response 3:

Thanks for your comments and suggestions. According to your suggestion, we have removed the last paragraph in Section 1.

Please see the Section 1 in the revised manuscript.

Point 4：

Figures, Equations, and Tables are not always recalled in the text (e.g., Figure 4, Table 1, Equation 1, etc.). In addition, they should be placed close to the text where they are discussed.

Response 4:

Thanks for your comments and suggestions. According to your suggestion, we placed the diagrams near the text where they were discussed, while putting the role of Figure 5, Table 1, and Equation 1 in the text.

Please see lines 104-105, 308-310 and 316-317 etc in the revised manuscript.

Point 5：

①Figure 1 please add a legend. Please check the Figure/Table numbering (i.e., Lines 107, 308, 323, and 372). ②Section 3.1: please check and update the manuscript according to the Journal template. ③The reviewer suggests improving the quality and readability of Figures 5 and 6

Response 5:

Thanks for your comments and suggestions. According to your suggestion, ① We have added the legend to Figure 1. ②We apologize for the fact that the chart serial numbers did not match in the paper due to our carelessness and that the formatting in section 3.1 was not correct with the template. In the revised version, we have checked all the chart serial numbers and their citations.

③We redrew Figures 5 and 6 to ensure the clarity of the images, and added vertical titles to Figure 5 and a Table 6 to Figure 6 for specific numerical presentation

Please see Figure 1、section3.1 and Figure 5、6. in the revised manuscript.

Point 6：

Lines 359-362: it is not clear the use of Python and Vissim

Response 6:

Thanks for your comments and suggestions. According to your suggestion, We describe in detail the specific use of python and vissim software in the simulation experiments

4.Simulation analysis

……..

The quantitative parameters such as the turning ratio at each intersection and the signal timing of non-critical intersections are input in this road network. Considering that the control scheme under the optimization scheme is a multi-time varying signal control, Vissim and Python are used to implement the signal control program under the optimization scheme in this paper. Firstly, the vissim software is used to construct the topology of the simulated road network, set up the phase and timing scheme of each intersection, input the original traffic flow obtained from the survey and the al-location of the steering ratio; secondly, on the basis of the completed vissim configura-tion, python is used for the secondary development of vissim to write the optimized control scheme implementation program. According to this control program, the sim-ulation time is taken as 3600s, and the operation on the road network is simulated. Based on the simulation results, the original timing control scheme and the optimized feedback control scheme are compared and analyzed by selecting delay time and stop time as the evaluation index.

……..

Please see section 4 in the revised manuscript.

Point 7：

The Conclusions section lacks in terms of numerical results

Response 7:

Thanks for your comments and suggestions. According to your suggestion, we have added the corresponding numerical results to the conclusion in order to express our content more visually

Conclusion

In this paper, an urban road network traction control method for critical intersections is designed by combining the characteristics of road networks. Firstly, an urban road network traction control model is established based on the general complex dynamic network state equation and its traction control model. The model considers the coupling relationship between intersections and road segments to establish, and introduces the degree of coupling and turning ratio to describe the interaction of traffic between key intersections and road segments. The degree of association is the reciprocal of the number of road sections between the road section and the key intersection and whether the traffic flowing through the key intersection flows into and out of the road section as the coupling between the road section and the key intersection, and the turning ratio is the product of the turning ratio of all intersections out of the shortest path when the traffic flows from the key intersection into and out of the road section. The parameter takes into account the control effect of key intersections on road sections will decrease with the growth of distance, and further proves that the road sections directly connected with key intersections should be the focus of monitoring in the paper.

………

Please see section 5 in the revised manuscript.

Author Response File: Author Response.pdf

Reviewer 4 Report

The study addresses an interesting and highly topical issue of urban traffic congestion mitigation.

The study is correct, but has shortcomings, which were pointed out in the comments.

I propose to rewrite the purpose of the paper, because now it gives the impression of being incorrect.

I have the impression that there is a redundant paragraph in the text.

I recommend pointing out the limitations of the study and inference, because there are, after all, quite a few of them....

Comments for author File: Comments.pdf

Author Response

Point 1：

I propose to rewrite the purpose of the paper, because now it gives the impression of being incorrect.

Response 1:

Thanks for your comments and suggestions. According to your suggestion, we reorganized the research objectives of the paper in Section 1.

1.Introduction

……..

The main work of this paper proposes a drafting control scheme considering feedback, by changing the green letter ratio of each phase at key intersections and achieving the purpose of changing the flow rate of each road section according to the correlation between key intersections and each road section, so that the road network as a whole reaches a new stable state. The traffic congestion is relieved with a smaller control cost and the operational efficiency of the road network is improved.

The specific work is as follows:

(2) A drafting control strategy is proposed to adjust the signal timing of key intersections by judging the operation status of traffic flow in each section of the road network so that all sections of the road network are in a smooth state

(3) Simulation of the drafting control strategy and method is carried out on the regional road network of Xin'an Street, and the results show that the proposed strategy can effectively reduce the delay and queuing time in the road network.

………

Please see section1 in the revised manuscript.

Point 2：

I have the impression that there is a redundant paragraph in the text

Response 2:

Thanks for your comments and suggestions. According to your suggestion, we removed redundant paragraphs from the paper in Section 3.3

Delete the following: “Manuscripts reporting large datasets that are deposited in a publicly available database should specify where the data have been deposited and provide the relevant accession numbers. If the accession numbers have not yet been obtained at the time of submission, please state that they will be provided during review. They must be provided prior to publication”

Please see section 3.3 in the revised manuscript.

Point 3：

I recommend pointing out the limitations of the study and inference, because there are, after all, quite a few of them

Response 3:

Thanks for your comments and suggestions. According to your suggestion, we describe the shortcomings in this paper and propose the next steps in the conclusion section of the paper.

Conclusion

Please see section5 in the revised manuscript.

Point 4：

Problems with markup in pdf files

Response 4:

Thanks for your comments and suggestions. Based on your suggestions for this paper in the pdf file, we have made the following changes

(1)In the last paragraph of the abstract, specific values for the network performance improvement under the control scheme are added

The results show that the average delay time and average stopping time of the road network are reduced by 35.03s and 18.37s, respectively, compared with the original control scheme, proving that the control strategy can effectively reduce congestion and improve the operational efficiency of the road network.

(2) In section1, we added the issue of traffic safety is also one of the prominent issues on traffic

However, considering the restrictive situation in terms of land use, laws and regula-tions, traffic safety issues and traffic congestion are still urgent challenges in many countries.

(3) We list the shortcomings of each of the two methods in reference [15]

Kouvelas et al. [15] propose a hybrid signal control strategy that integrates TUC and DB strategies, since the DB method is only applicable to unsaturated traffic conditions and the TUC method is applicable to saturated traffic conditions, the paper mixes the two methods to improve the control of the network

(4)Adjusted the description of Figure 1 to the top of the image

The controlled inflow to and outflow from section j for the adjacent sections of section receiving the corresponding intersection is illustrated in Figure 1.

Figure 1. Schematic diagram of vehicle inflow and outflow in section

（5）One of the most important goals was described with emphasis on solving the congestion on the roadway.

Since the actual state of the road network may be that some sections have too much traffic causing congestion, while some sections have little traffic causing poor utilization of road resources, it is necessary to adjust the operation of the entire region, the most important of which is to adjust the congested sections directly connected to key nodes as well as other congested sections, and control the traffic diversion from congested sections to other sections with low traffic volume to ensure the balance of the entire road network.

（6）The purpose of the control in the proposed section 3.3 is to change the flow of the congested section and reduce the delay time

The main objective of the pinning control in this paper is to change the traffic flow on congested road sections and reduce the delays on the road network. It is ensured that the utilization of the roads reaches a good state, i.e., the network is guaranteed not to generate congestion, while the utilization of the road sections in the network is not too low; the traffic flow on the road sections can reach a desirable state.

（7）This is such a highly simplified situation. What about the situation when there is also a traffic jam on the cross roadway? Increasing the green light time on one roadway will increase the traffic jam on the cross roadway.

We initially judged the congestion of the roadway when we selected the control node. The congested roadway around the intersection indicates that the intersection has a significant impact on the traffic in the area. Therefore, when we implement the control scheme, we first consider relieving the congestion on the road sections directly connected to the key intersection, and on this basis, we then consider regulating the congestion on other road sections.

（8）Adjusted the chart number and the corresponding citation section

Figure 5.3 and Table 5.4 cited in the paper were changed to Figure 4 and Table 3

（9）Considering that the flow of traffic takes a certain amount of time, the description is changed to be able to achieve the purpose of reducing the flow of congested road sections.

It can quickly reduce traffic flow on congested roadways directly connected to critical intersections, and on top of that, further reduce congestion on roadways further away from critical intersections.

（10）The narrative of the conclusion was changed, while the shortcomings of this paper were added as an outlook for future research.

Conclusion

Please see the revised manuscript.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors addressed all suggested changes. I accept the current version.

Please check if you can't correct the grammar in a few places, it's about commas, that is:

Commas are most commonly used in the following contexts: To separate component clauses (i.e. the "parts" of a complete sentence that contain a subject and a verb), especially when they are connected with and, but, so, or, nor, yet or for.

Author Response

Thanks for your comments and suggestions. According to your suggestion，we read through the entire text and corrected the use of inappropriate commas.

Reviewer 3 Report

In general, I think the work is well designed and written

Author Response

According to your suggestion, we have added some examples of the application of the pinning control method in recent years.

1.Introduction

………….

In recent years, pinning control methods have been applied in different fields. Li et al. designed a pinning controller that saves control costs and resources while guaranteeing the horizontal performance of complex networks. Jia et al. by designing the starting conditions of different control signals, the sufficient conditions for achieving network synchronization with minimum control cost are investigated by applying drives to some nodes under the dynamic pinning control strategy so as to achieve the pinning synchronization problem in response to the whole network. Lu et al. investigates the stability of Boolean control networks under pinning control, verifies the stability of the network by Warshall algorithm, and also calculates the minimum set of pinning control nodes in the present time. Wang et al. considers pinning control and adaptive pinning control to study the time synchronization of BAM networks with time-varying delays. The pinning control mechanism for some nodes enables the network to derive new sufficient conditions to achieve time synchronization, verifying the effectiveness and feasibility of the network to achieve synchronization under pinning control. Andoh et al. proposes a hierarchical pinning control method, which makes the number of pinning nodes smaller by selecting the most appropriate pinning nodes, while enabling the multi-agent system to reach consensus, and applies it to vehicle platooning. In 2018, Wang et al. considered the dynamic performance of the traffic network to construct a complex traffic network model and demonstrated that the complex traffic network can reach the state of synchronization criteria through tethered control by studying the degree of the network and the selection of control nodes under the energy index of a single node. Zheng et al. applied the theory of traction control to control urban traffic networks by constructing controllers with road sections as units, so that the flow in the network can reach an equilibrium state. The urban road also has typical small world effect and scale-free effect, so this paper introduces pinning control for the study.

The specific work is as follows:

Please see the Section 1 in the revised manuscript.

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Research on Urban Road Traffic Network Pinning Control Based on Feedback Control

The research is considered as the simulation and applied verification of a traffic regulation model based on fixation control, based on the proposals extracted from the background literature review

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