Entropy Model of Dynamic Bus Dispatching Based on the Prediction of Back-Station Time

Round 1

Reviewer 1 Report

Bus dispatching is widely studied over the world, the main challenge of bus dispatching is the uncertain factors from bus operation, traffic signal timing and traffic congestion. High quality real-time prediction of bus arriving time might contribute to robust bus schedule. This paper proposed an optimization model using entropy theory for improving the operation performances of public transit system. The comments of the current manuscript are as follows.

1, The framework of this paper should be improved. Specifically, a flowchart can be used in section 2. In addition, the prediciton of bus travel time is absent.

2, As to the OR model in section 3, the authors should point out the decision variables, and how bus travel time can be integrated in this model. 

3, I have to say, the relationship between bus dispatching and travel time prediction is unclear. The authours are suggested to strengthen the modeling and discussion on predition.

4, There is no dynamic equation on bus system, the reviewer will wonder how the authors can compute the specific data and results in section 4. 

5, The settings and related procedure for the simulated or numeraical experiments should be addressed in section 4, as readers cannot understand the running of bus ststem in the given two examples.

6, The contribution of this paper on the methodology in the filed of bus schedule or dispatching should be improved.

Author Response

1.The framework of this paper should be improved. Specifically, a flowchart can be used in section 2. In addition, the prediction of bus travel time is absent.

Response: We added a methodology flowchart in section 2. The absence of the prediction of bus travel time due to there have been abundant studies on travel time prediction already and our study mainly focus on the issue of bus dispatching, so the prediction of bus travel time is not involved in this paper.

2. As to the OR model in section 3, the authors should point out the decision variables, and how bus travel time can be integrated in this model.

Response: The decision variable has been pointed out at the middle of section 3.1. The decision variable  is the normalized value of change rate of bus departure interval before and after adjustment, which is defined in Equation (2.10); Because we mainly focus on the issue of bus dispatching, so the bus travel time is not considered in the model.

3.I have to say, the relationship between bus dispatching and travel time prediction is unclear. The authors are suggested to strengthen the modeling and discussion on prediction.

Response: Because we mainly focus on the issue of bus dispatching, so the bus travel time is not considered in the model.

4.There is no dynamic equation on bus system, the reviewer will wonder how the authors can compute the specific data and results in section 4. 

Response: We used real historical data as the prediction result of travel time to get the calculation result based on it, and we have added the explanation it in section 4.

5. The settings and related procedure for the simulated or numerical experiments should be addressed in section 4, as readers cannot understand the running of bus system in the given two examples.

Response: Because the problem studied is relatively simple, we used the software of Lingo to solve it. Lingo is a very classic comprehensive tool for solving linear programming, quadratic programming, integer programming and nonlinear programming optimization problems. It has a series of completely built-in solving procedures, and can automatically select the appropriate solver by reading the equation, which is suitable for solving the model in this paper

6.The contribution of this paper on the methodology in the field of bus schedule or dispatching should be improved.

Response: We added the analysis of bus departure delay in section 2 to further illustrate the role of this study.

Author Response File: Author Response.docx

Reviewer 2 Report

This paper builds a entropy model of dynamic bus dispatching based on prediction of back-station time, which can be used to decreasing the passive effect of discontinuity by extending the departure interval of the early bus in advance, and to realize the fairness on adjustments of the departure interval by using entropy theory. The topic addressed in the paper is of interest to the special issue and the journal, and the paper is well structured. Please find my comments below:

1. Dynamic bus dispatching is an active area. Please provide more recently published relevant literature.

2. It is necessary to further analyze the advantages of information entropy compared with other models and parameters according to the problem discussed in this paper.

3. This paper should enhance the methodological framework and discuss in more detail the policy implications of the results obtained in example analysis

4. English in this paper needs to be thoroughly checked and carefully revised, including the numbering and quotation of tables and formulas.

Author Response

1.Dynamic bus dispatching is an active area. Please provide more recently published relevant literature.

Response: We added 5 references on dynamic bus dispatching, which have been marked in red.

2.It is necessary to further analyze the advantages of information entropy compared with other models and parameters according to the problem discussed in this paper.

Response: We have added the advantage of information entropy model at the end of section 5. Compared with other models, the advantage of entropy model is that it does not need to standardize data when measuring data volatility, which solves the problem that other models need to ensure data consistency when using

3.This paper should enhance the methodological framework and discuss in more detail the policy implications of the results obtained in example analysis.

Response: We added the analysis of bus departure delay, research objectives, ideas and a methodology flowchart in section 2, 3 in order to enhance the framework.

4.English in this paper needs to be thoroughly checked and carefully revised, including the numbering and quotation of tables and formulas.

Response: We have checked the English in this paper and corrected those misused label numbers. The revisions are marked in red.

Author Response File: Author Response.docx

Reviewer 3 Report

In their manuscript, the authors tried to provide a solution to an important task in the field of public transportation system. The topic is current, but it is necessary to improve the manuscript for publication. Below are suggestions and questions that authors may find helpful:

-  In the introduction, it is desirable to expand the topic towards the sustainability of bus transportation, of course with more recent references. Also, it would be good to find additional, more recent references (e.g., related to bus scheduling) if they exist;

 -  In the discussion or introduction, state how the application of the proposed model can affect the dimensions of sustainability in reality (economic, ecological and social); 

- Are there any studies on users' attitudes about this way of functioning bus transportation?

 -     Are the data for examples 1 and 2 obtained from a real system? What territory does the case study cover? If possible, it would be good to show a map of the territory with the associated network and transport lines;

-   It would be good to improve the discussion within examples 1 and 2 and additionally point out the positive and negative effects of applying the proposed model…;

- It is desirable to improve the conclusion in accordance with the previous point... 

 

Author Response

1.In the introduction, it is desirable to expand the topic towards the sustainability of bus transportation, of course with more recent references. Also, it would be good to find additional, more recent references (e.g., related to bus scheduling) if they exist;

Response: We added 5 references on dynamic bus dispatching, which have been marked in red.

2.In the discussion or introduction, state how the application of the proposed model can affect the dimensions of sustainability in reality (economic, ecological and social); 

Response: We have added the explanation of the research results of this paper for improving the public transport service level, alleviating the in-car congestion, and improving the public transport travel sharing rate in discussion.

3.Are there any studies on users' attitudes about this way of functioning bus transportation?

Response: We have found some studies on users’ attitudes on dynamic bus scheduling generally but we are afraid no more relevant research about this way of functioning bus has been found yet.

4.Are the data for examples 1 and 2 obtained from a real system? What territory does the case study cover? If possible, it would be good to show a map of the territory with the associated network and transport lines;

Response: The data for the two examples are both from a bus line in Guangzhou, China. We added a schematic map of the bus line at the beginning of the section 4, which shows the shape of the line and its surrounding area.

5.It would be good to improve the discussion within examples 1 and 2 and additionally point out the positive and negative effects of applying the proposed model.

Response: We added the discussion of the advantages and disadvantages of the model in the end of section 5.

6.It is desirable to improve the conclusion in accordance with the previous point.

Response: We also added the analysis of the advantages and disadvantages of the model in conclusion.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have addressed the reviewer's comments. It'll be better that the authors can improve the English writting.  

Reviewer 3 Report

Dear authors,

I am satisfied with your answers and explanations. We await the results of your future research.