The Method of Trajectory Selection Based on Bayesian Game Model
Round 1
Reviewer 1 Report
The overall quality of the work is good, here are some remarks and questions to the authors:
(1) Section 1: Introduction. Page 2: The abbreviation, TOS, should be interpreted the time it first appears. I proposed a switch of the definition in the first paragraph of Section 2, page 3, to the first time TOS occurred for a better understanding
(2) Section 5: Experiment analysis. Page 6: The legend in Figure 2 needs some modifications. You repeated FCA_ZSHA_001 twice in the legend.
(3) Section 5: Experiment analysis. Page 7: For the number of most likely arrival times, why three? Additional explanations will appreciate.
(4) Section 5: Experiment analysis. Page 8: What is the criterion of grouping?
(5) Section 5: Experiment analysis. Page 8: Define congestion period will improve the readability.
(6) Section 5: Experiment analysis. Page 11: The subtitle of Figure 6 should be consistent with the description in the text.
(7) Section 6: Conclusions. Page 14: It is advisable to make some statements about the limitation of your research to further complete your paper, maybe in your conclusion part or start a new chapter. You have made some assumptions when you considering the practical situation in Section 5, page7, so you must have something to say about your research limitations.
(8) The reference about Trajectory Preference Selection Model and Bayesian Game Model be further cited as following papers:
Ye, X.; Sui, X.; Wang, T.; Yan, X.; Chen, J. Research on parking choice behavior of shared autonomous vehicle services by meas[1]uring users’ intention of usage. Transp. Res. Part F Traffic Psychol. Behav. 2022, 88, 81–98. https://doi.org/10.1016/j.trf.2022.05.012.
Liu, L.; Ye, X.; Wang, T.; Yan, X.; Chen, J.; Ran, B. Key Factors Analysis of Severity of Automobile to Two-Wheeler Traffic Accidents Based on Bayesian Network. Int. J. Environ. Res. Public Health 2022, 19, 6013.https://doi.org/10.3390/ijerph19106013
Please consider these questions/comments and update the manuscript accordingly.
Author Response
Thanks for your review! The author has revised the paper based on your suggestions, here are the responses to your points.
Point 1:
Section 1: Introduction. Page 2: The abbreviation, TOS, should be interpreted the time it first appears. I proposed a switch of the definition in the first paragraph of Section 2, page 3, to the first time TOS occurred for a better understanding
Response 1:
The definition of TOS has been adjusted to section I. (Page 2 line 58-62).
Point 2:
Section 5: Experiment analysis. Page 6: The legend in Figure 2 needs some modifications. You repeated FCA_ZSHA_001 twice in the legend.
Response 2:
The legend in the Figure has been modified. (Page 7 Figure 3).
Point 3:
Section 5: Experiment analysis. Page 7: For the number of most likely arrival times, why three? Additional explanations will appreciate.
Response 3:
The description of the data source and the reason for selecting the data has been added to the paper. (Page 8 line 253 -260).
The reason for choosing the three arrival times is that these times are the three time points at which the flight is most likely to arrive at FCA after calculation. In addition, the more time points, the more strategy sets for the game model, which will cause that the complexity of calculation is greatly increased. So selecting three time points is a comprehensive consideration of the calculation and the actual situation, which is more appropriate.
Point 4:
Section 5: Experiment analysis. Page 8: What is the criterion of grouping?
Response 4:
Firstly, the purpose of grouping is to avoid too many participants (i.e., type sets) leading to too large a calculation scale. Secondly, considering the habit of Chinese control operation, the management is usually conducted with 15 minutes as the time window. Therefore, the flights are sorted according to the time when the flights fly by the point UGAGO and grouped at a fixed time interval (15 minutes) to facilitate calculation. At the same time, the fixed time interval also facilitates the subsequent measurement of the impact between each group of flights.
Point 5:
Section 5: Experiment analysis. Page 8: Define congestion period will improve the readability.
Response 5:
The definition of the congestion period has been added in the paper to improve readability. (Page 9 line 275-278).
Point 6:
Section 5: Experiment analysis. Page 11: The subtitle of Figure 6 should be consistent with the description in the text.
Response 6:
The description of the subtitle of the Figure in the paper has been modified to be consistent with the Figure. (Page 12 line 349-362).
Point 7:
Section 6: Conclusions. Page 14: It is advisable to make some statements about the limitation of your research to further complete your paper, maybe in your conclusion part or start a new chapter. You have made some assumptions when you considering the practical situation in Section 5, page7, so you must have something to say about your research limitations.
Response 7:
The limitations of the research have been supplemented in the conclusion of the paper. (Page 16 line 471-478).
Point 8:
The reference about Trajectory Preference Selection Model and Bayesian Game Model be further cited as following papers:
Ye, X.; Sui, X.; Wang, T.; Yan, X.; Chen, J. Research on parking choice behavior of shared autonomous vehicle services by meas[1]uring users’ intention of usage. Transp. Res. Part F Traffic Psychol. Behav. 2022, 88, 81–98. https://doi.org/10.1016/j.trf.2022.05.012.
Liu, L.; Ye, X.; Wang, T.; Yan, X.; Chen, J.; Ran, B. Key Factors Analysis of Severity of Automobile to Two-Wheeler Traffic Accidents Based on Bayesian Network. Int. J. Environ. Res. Public Health 2022, 19, 6013.https://doi.org/10.3390/ijerph19106013
Response 8:
The latest relevant research results have been supplemented in the introduction of the paper. (Page 2 line 54-57).
Thank you again for your points makes the paper more reasonable.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
1. The purpose of the paper is to improve the fairness of en-route resource allocation and meet airline's trajectory preference, but the case analysis does not clearly reflect its fairness, what is the standard for evaluating fairness?
2. In addition, the comparison taken here is between the results obtained by the established model and the results obtained by mathematical analysis, and the comparison with other research results is lacking, so the clarification is weak.
3. The article lacks the detailed description of the practical significance of this method, and the importance of the practical significance. Therefore, the trajectory selection method proposed in this paper is innovative and scientific, but it is weak in the case results and has unclear practical significance.
4. In the case, when the game model is established to determine the parameters of the Type set and the Strategy set, why are Airlines classified as a single participant instead of a single flight?
5. The representativeness of the experimental design needs to be explained.
6. In Section 2: Analysis of the construction of the Trajectory Preference Selection Model, there is a factor M missing from the elements of the Bayesian model.
7. Table 2 reliability of data source of affected flight information? Why does the expected entry time FCA2 always differ from FCA1 by five minutes? What is the relationship between FCA 1 and FCA 2?
8. In table 5. Please explain the meaning of none and not.
9. The clarity of figure 6 needs to be improved.
Author Response
Thanks for your review! The author has revised the paper based on your suggestions, here are the responses to your points.
Point 1:
The purpose of the paper is to improve the fairness of en-route resource allocation and meet airline's trajectory preference, but the case analysis does not clearly reflect its fairness, what is the standard for evaluating fairness?
Response 1:
Although there is no specific data about fairness in case analysis, the fairness is not an intuitive data result but is reflected in the construction process of the whole model. First of all, this study discusses the game between airlines, and the deep connotation of the game is to take fairness as the core. Specifically, in the game process, this study conducts the game from the perspective of each airline, i.e. taking each airline as an independent participant and other airlines as another participant in turn to obtain the upper limit of delay of the airlines’ guarantee strategies. This process is equivalent to that each airline can take turns to be the host, so as to ensure the fairness of the whole process. Secondly, the fairness of this study is compared to considering the efficiency from the overall perspective, which not only needs to achieve the goal of minimum total delay time, but also ensure the delay time of each airline, and then the resource allocation process is fairer.
Point 2:
In addition, the comparison taken here is between the results obtained by the established model and the results obtained by mathematical analysis, and the comparison with other research results is lacking, so the clarification is weak.
Response 2:
The comparative experiment results and relevant analysis have been supplemented in the paper. (Page 14 line 387-394).
From the supplementary data, it can be seen that the guarantee strategy obtained by using the game theory method proposed in this paper is lower than the upper limit value of any other strategy (the calculation of these arbitrary strategies is based on the results of other existing research methods: FCFS, Multi-objective Programming, Two-stage Framework, and RBS), and it is more robust, which can explain the effectiveness of this method.
Point 3:
The paper lacks the detailed description of the practical significance of this method, and the importance of the practical significance. Therefore, the trajectory selection method proposed in this paper is innovative and scientific, but it is weak in the case results and has unclear practical significance.
Response 3:
The practical application significance of the method is to combine with the subsequent multi-objective optimization results (as shown in the figure in the uploaded file). We can select the allocation scheme that meets the requirements of the guarantee strategy among the many Pareto frontiers, so as to make the resource allocation fairer and more conducive to the decision-making of the air traffic controllers.
For example, there are 16 noninferior solutions in the figure, and the air traffic controllers may need to randomly select an allocation scheme from them, but the scheme may not be optimal. At this time, the scheme meeting the guarantee strategy requirements can be selected from 16 noninferior solutions according to the game results, so as to narrow the selection range and make the final distribution scheme fairer.
Point 4:
In the case, when the game model is established to determine the parameters of the Type set and the Strategy set, why are Airlines classified as a single participant instead of a single flight?
Response 4:
Because the research is based on the implementation process and characteristics of CTOP, aiming at improving the fairness between airlines in the process of resource allocation. It considers the game process between airlines, so modeling with airlines as participants.
In addition, if each flight is classified as the object to participate in the game, this will result in a very large scale of calculation. At the same time, the game is played in too many rounds, which will result in the final failure to obtain the allocation strategies that can meet all flights’ requirement.
Point 5:
The representativeness of the experimental design needs to be explained.
Response 5:
The basis of the experimental design has been supplemented in the paper. (Page 3 line 107-115)
Point 6:
In Section 2: Analysis of the construction of the Trajectory Preference Selection Model, there is a factor M missing from the elements of the Bayesian model.
Response 6:
The analysis of the factor M has been supplemented in Section 3 of the paper. (Page 4 line 178-184).
Point 7:
Table 2 reliability of data source of affected flight information? Why does the expected entry time FCA2 always differ from FCA1 by five minutes? What is the relationship between FCA 1 and FCA 2?
Response 7:
The data source and selection basis have been supplemented in the paper. (Page 8 line 253 -260).
Because this time is related to the length of the flight segment, and due to the geographical location between the two FCAs, the length difference between the two flight segments is a fixed value, which causes the difference in the expected entry time of two FCAs to be a fixed value (i.e. 5 minutes)
Point 8:
In table 5. Please explain the meaning of none and not.
Response 8:
These two words have the same meaning, and have been uniformly revised. The meaning of data has been supplemented in the paper. (Page 15 line 442-443).
The delay value is none, which means that there is no flight of the airline in this group, so there is no calculation result of the airline.
Point 9:
The clarity of figure 6 needs to be improved.
Response 9:
The Figure has been modified in the paper and replaced with the figure with higher definition. (Page 12 Figure 7)
All of the sentences in the paper have been carefully read and revised by the author. The grammatical errors should have been corrected in the revised manuscript.
Thank you again for your points makes the paper more reasonable.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments for author File: 
Comments.docx
Author Response
Thanks for your review! The author has revised the paper based on your suggestions, here are the responses to your points.
Point 1: Has the experiment (conducted in April 2019) not been influenced by the COVID-19 pandemic phenomenon and the associated reduction in flights and passenger numbers worldwide?
Response 1:
Because the method proposed in this paper is aimed at the fairness of resource allocation among airlines during the implementation of the new traffic management initiative -CTOP, and mainly considers the operation state under the normal environment of airspace. The typical operation state in April 2019, which was not affected by extreme weather and the COVID-19, was selected for research. Combined with the actual traffic demand, the research on this typical operation state is more valuable.
Although the current epidemic has a great impact on civil aviation operations, according to the prediction of the Civil Aviation Administration of China (CAAC), the impact of the epidemic may be basically eliminated in about two years (i.e. the spring of 2023), so it is more meaningful to study the situation without the impact of the epidemic in the future.
Thank you again for your points makes the paper more reasonable.
Round 2
Reviewer 2 Report
Accept.
