Signal Control Study of Oversaturated Heterogeneous Traffic Flow Based on a Variable Virtual Waiting Zone in Dedicated CAV Lanes
Round 1
Reviewer 1 Report
Your paper contained an analysis of a very interesting idea evaluated with appropriate simulations. I read it with great interest. However, the following two points should be corrected for the benefit of future readers.
1) The resulting figures (especially 17 - 25) are too small to read the information in the text.
Also, the relationship between the quantities is hard to read, so I would prefer you to make it easier to read, e.g. change some numbers to ratios.
2) Regarding the explanation of the results in section 5, the difference between the two performances is well understood. However, I feel that the explanation of the mechanism of the difference is lacking. It would be preferable to have a discussion of the main reason why the VVWL control mode is better while presenting more detailed simulation results.
For example, why do the nonlinear changes in Figure 20 (b) occur?
Author Response
Comment No.1：The resulting figures (especially 17 - 25) are too small to read the information in the text. Also, the relationship between the quantities is hard to read, so I would prefer you to make it easier to read, e.g. change some numbers to ratios.
Response: Thank you very much for helping me correct the deficiencies in the composition of the paper layout. I have rearranged the pictures 17-25 according to your tips. The relationship between the quantities you mentioned is difficult to read. It is suggested that I change it to the ratio. I also made the change.
Comment No.2：Regarding the explanation of the results in section 5, the difference between the two performances is well understood. However, I feel that the explanation of the mechanism of the difference is lacking. It would be preferable to have a discussion of the main reason why the VVWL control mode is better while presenting more detailed simulation results. For example, why do the nonlinear changes in Figure 20 (b) occur?
Response: Thank you very much for your valuable suggestions. As you described, you want me to make comments and in-depth analysis on the difference mechanism. I very agree with your suggestions. Therefore, this paper analyzes the advantages of the model from the perspectives of saturation, CAV permeability, left-turn CAV ratio and variable virtual waiting zone length, and analyzes the reasons in detail at the result end. The reason for the difference mechanism is that the variable virtual waiting zone makes full use of the intersection zone from the theoretical side, and can reduce the time of signal control, so as to shorten the entire cycle length of the intersection, The purpose of time and space conversion is achieved, and the space-time resources of the intersection are fully utilized. This point is highlighted in 5.3.4. As for the reason why nonlinear changes occur in Figure 20(b) you mentioned, the reason is that I sampled and simulated the permeability of CAV, resulting in a breakpoint change in the result, and the reduction of HV permeability will also affect vehicle delay, which is directly related to the driver simulation model, so the result of nonlinear changes will occur.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Please see the PDF attached.
Comments for author File: 
Comments.pdf
Author Response
Comment No.1：Page 4: It is unclear to me how some of the assumptions made could hold. For assumption (1), how can you obtain the information of HVs in the future cycle? For assumption (3), how can you obtain the arrival rate of HVs? Would steady arrivals indicate a constant arrival rate？
Response: I'm sorry that my statement is not clear enough, resulting in incomplete assumptions. Since this paper focuses on the traffic problem of oversaturated heterogeneous traffic flow, the default HV will not change lanes after entering the adjustment zone. Since there is a CAV lane near the intersection, this indirectly forms the HV lane near the intersection, and also contributes to the formation of HV fleets. Due to the relatively long length of the adjustment zone, high-pressure vehicles cannot be completely released in a cycle. In the second hypothesis, the queue length and traffic speed of high-pressure vehicles can be detected by the basic detection equipment by default. This provides the possibility to predict the arrival information of HV in the future cycle. Therefore, this paper modifies the first assumption as follows: HV does not change lanes in the adjustment area and the exclusive lane area, and can collect or predict the arrival information of CAV and HV at the intersection in the next signal cycle. Delete the third assumption.
Comment No.2: Page 6: The authors claim that “How CAVs and HVs enter the intersection at future time T is used as the input to the control model.” While you may be able to obtain some information of CAVs using connectivity, how would that work for HVs? Also, there is a limit on CAV communication ranges, which determines how much information of CAVs can be accessed over a certain period of time.
Response: Thank you very much for raising this question, which gives me the opportunity to further explain the value of CAV lane. As the answer to the first question, this paper proposes in hypothesis 1 that HV does not change lanes in the adjustment zone and the passing zone, and the adjustment zone is relatively long. In the case of oversaturation, HV fleets in the adjustment zone cannot be fully released in a cycle, and the adjustment zone is equipped with basic sensing equipment, which can sense the length and speed of CAV fleets and HV fleets. This is helpful for predicting CAV and HV.
Comment No.3：Page 10: In equation (8), is the arrival rate considered deterministic or stochastic? It appears that you solve a deterministic optimization problem using dynamic programming (DP), while emphasizing stochastic demand. In fact, one needs 1 to apply a Monte Carlo method when using DP to solve a stochastic optimization problem.
Response: Thank you very much for asking this question. The arrival rate of vehicles in this article is random, but this paper assumes that the arrival of HV can be predicted in advance, which has been modified in the assumption. Thank you again for correcting this problem, so on the whole, this is a deterministic dynamic programming problem, without random interference variables. Therefore, under the premise of emphasizing stochastic demand, this paper adopts dynamic programming (DP) method to solve the deterministic optimization problem, and the optimization is still the control sequence. As described in the modeling process of the upper model in this paper, the signal optimization of the upper layer is modeled as a discrete-time dynamic programming problem. Your idea of using Monte Carlo method to solve the problem is very worthy of adoption, so it has been used in the signal control of heterogeneous traffic flow based on pre-signal light that I am writing.
Comment No.4：Page 14: In equation (32), vehicle acceleration can only take three possible values. Why don’t you consider a general case of ?
Response: Thank you very much for raising this valuable question, which is of great practical significance, because the acceleration of vehicles in real life must be a random value generated between , and it is better to improve the fuel economy. However, this paper focuses on how to improve the signal control quality of intersections in the face of oversaturated heterogeneous traffic flow, and does not consider vehicle comfort and fuel economy as optimization objectives. Therefore, this problem is simplified, which is also explained in 4.3.2 of this paper, which is also the method commonly used by many peers. However, I am currently working on the article of CAV trajectory optimization and intersection signal control, which focuses on the acceleration of vehicles. Thank you again for your very practical suggestions.
Comment No.5：Page 14: In Figure 11, the value of is simply a constant, specifically, = 0.
Response: You observe the problem very carefully, which requires special learning and respect. As you mentioned, in Figure 11, The value of is only a constant. Specifically, =0. The reason for setting =0, which is to simplify the acceleration state of the vehicle, namely acceleration, constant speed (or stationary) and acceleration, which is also the method commonly used by many peers. This is similar to your previous question. Thank you for your valuable suggestions. I hope you will be satisfied with my answer.
Comment No.6：Page 15: The authors claim that “ and are the upper and lower limits of , respectively.” So, is always no less than ? In that case, the max operator in equation (42) would simply give you at all times? That does not appear to be correct.
Response: Thank you very much for raising this question. I can see that you are serious and rigorous. Here, this paper quotes the vehicle following model in the fleet commonly used by peers to update the vehicle track, that is, the next generation simulation (NGSIM) vehicle following model to update the vehicle track. This model has additional safety constraints to avoid collisions, and it also considers vehicle performance limitations, such as maximum acceleration and deceleration rates. The you mentioned refers to the maximum acceleration distance of the vehicle under the premise of ensuring safety constraints, refers to the maximum deceleration distance of the vehicle under the premise of ensuring safety constraints. Because the vehicle is not always in the acceleration state during the following process of the fleet, it will also slow down. Therefore, formula 42 refers to the maximum distance that can be reached if the vehicle is in the following state in the fleet, and the shortest distance that can be achieved if the fleet is in the accelerating state. So the operator is not always in status. I hope you are satisfied with my explanation. Thank you again for raising this question.
Comment No.7: Page 16, line 582: should be .
Response: Thank you very much for the mistake you pointed out. I'm sorry that it was caused by my carelessness. Now it has been corrected. Thank you again for your reminder.
Comment No.8: Page 16: The maximum speed limit for CAVs is 14 for the simulation. This does not appear to be realistic since the speed limit is too small.
Response: Thank you very much for questioning this detail. The reason why this paper sets the maximum speed limit of CAV at 14m/s, that is, 50.4Km/h, is that this paper focuses on the signal control of oversaturated heterogeneous traffic flow at intersections in urban environment. According to the currently available urban road speed limit data, it is found that the urban speed limit is between 30 and 60 Km/h, and the occurrence of oversaturated traffic flow will lower the maximum speed. In view of this, the maximum speed limit of CAV is set at 14m/s. At the same time, in order to better verify the effectiveness of the signal control method of supersaturated heterogeneous traffic flow based on the variable virtual waiting zone of the CAV dedicated lane proposed in this paper, the selected reference document also sets the CAV maximum speed limit at 14m/s. Therefore, this paper believes that this can more intuitively reflect the effectiveness of the algorithm in this paper.
Comment No.9: Page 17, line 635: The authors claim that “The arrival information of each CAV within the predicted range is available through communication methods.” Did the authors consider the limit of CAV communication ranges?
Response: Thank you very much for your question about this detail. When making assumptions, this paper pointed out that there are basic sensing devices, namely roadside devices, in the control area and the dedicated lane area. These devices can communicate with CAV instantly. As stated in the introduction of this article, we believe that with the development of communication technology and perception technology, the Internet connected autonomous vehicle will be given more functions. The focus of this paper is to study in advance the possible problems of future autonomous vehicle on the road, so it is advisable to make modest assumptions in this paper.
Comment No.10: In Section 5, the authors have presented results for both uniform and stochastic arrival of vehicles. However, the optimization problem considered in Section 4 appears to be deterministic. It would be more clear to explicitly point out how the optimization problem is solved in the presence of stochastic demand. For example, the following papers have touched upon stochasticity of microscopic traffic simulation models and traffic demand.
Response: Thank you very much for your question about the source of simulation data. The reason why this paper chooses to use Poisson distribution arrival and average distribution arrival for data analysis is from the perspective of traffic flow theory. In order to avoid congestion in local sections and local periods, the traffic flow will be evenly divided, which often occurs in the urban traffic network. Under the condition that there is no manual intervention in the upstream and downstream of road traffic, according to the statistical data, the traffic flow distribution conforms to Poisson distribution. This is why this paper analyzes the data from the perspective of uniform distribution and Poisson distribution. This is also a common traffic flow control data source in the industry. In this paper, the deterministic dynamic planning problem is solved through the dynamic planning algorithm, because the arrival of HV and CAV fleets in the future cycle can be predicted in advance. This does not conflict with the law of vehicle arrival, so it is reasonable in theory and method. This paper focuses on traffic flow control when doing signal control, but there is a lack of attention to microscopic vehicle model. Therefore, the key documents you mentioned have great reference and learning value. Considering the randomness of microscopic traffic simulation model and traffic demand, it can indeed reduce fuel consumption and emissions to the greatest extent. This issue has also become the core innovation point of my thesis.
Comment No.11: There are a series of English errors throughout the manuscript.
Response: Thank you for pointing out the mistakes in my language writing. I have corrected and highlighted them.
Author Response File: Author Response.docx
Reviewer 3 Report
the article showcases the problem statements in a structured manner and the respective solutions are presented in efficient way .
Author Response
Thank you very much for your affirmation of my thesis, and I would like to express my heartfelt thanks again for your encouragement.
Round 2
Reviewer 2 Report
Thank you for revising the manuscript. It is now clear that you considered a stochastic model due to random vehicle arrivals, but the formulated problem was solved using dynamic programming in a deterministic fashion. This is fine for illustrative purposes in the numerical results section, but needs to be made clear in the manuscript.
To make the reference list complete, the papers on traffic control considering stochastic arrivals (mentioned in Comment #10 of the previous-round review report) shall be included in the revised manuscript since they are very relevant to what's considered in your study.
Thank you!
Author Response
Cover letter
Dear reviewer and editor:
On behalf of myco-authors, we are very grateful to you for giving us an opportunity to revise our manuscript. we appreciate you very much for your positive and constructive comments and suggestions on our manuscript entitled “Signal control study of oversaturated heterogeneous traffic flow based on a variable virtual waiting zone in dedicated CAV lanes”(ID: applsci-2121477).
We have studied reviewers' comments carefully and tried our best to revise our manuscript according to the comments. The following are the responses and revisions I have made in response to the reviewers' questions and suggestions on an item-by-item basis. Thanks again to the hard work of the editor and reviewer!
Response to the comments of Reviewer #2
Comment No.1：Thank you for revising the manuscript. It is now clear that you considered a stochastic model due to random vehicle arrivals, but the formulated problem was solved using dynamic programming in a deterministic fashion. This is fine for illustrative purposes in the numerical results section, but needs to be made clear in the manuscript.
To make the reference list complete, the papers on traffic control considering stochastic arrivals (mentioned in Comment #10 of the previous-round review report) shall be included in the revised manuscript since they are very relevant to what's considered in your study.
Thank you!
Response: Thank you very much for your second review of my paper and your valuable suggestions in a very short time. I have supplemented the paper and added three highly relevant references according to your suggestions. Thank you again for your guidance on my thesis.
