Modelling and Forecasting Passenger Rail Demand in Slovakia Under Crisis Conditions with NARX Neural Networks

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript addresses the modelling and simulation of rail passenger transport demand in the Slovak Republic under crisis conditions, using COVID-19 as a case study. The research topic is relevant and has practical significance for transport resilience planning. The dataset is comprehensive, and the application of a NARX neural network framework is appropriate. However, in its current form, the paper requires significant revisions before it can be considered for publication.

Major Concerns and Suggestions

1. Mismatch between Title and Content

The title suggests that the study involves simulation of the railway system, yet the content focuses solely on passenger demand modelling using NARX networks. No actual railway system simulation (e.g., operational adjustments, timetable scenarios, capacity flow simulation) is presented. The title should be revised to better reflect the scope of the study.

2. Figures

The resolution of many figures is too low, making them difficult to read. All figures should be redrawn or exported at publication-quality resolution.

Sub-figures lack proper labeling (e.g., (a), (b), (c)), which complicates cross-referencing in the text. Please revise accordingly.

3. Figure Analysis

The discussion of figures is largely descriptive. The paper lacks deeper interpretive analysis and summary of what each figure implies about system behavior. For example, Figures 9–18 present trends, but the authors provide only superficial comments. More critical comparisons, synthesis, and implications should be provided.

4. Code and Methodological Transparency

The manuscript contains screenshots of MATLAB code that are not clear enough for readers to interpret. Screenshots are not acceptable for publication-quality presentation. Instead, the algorithm should be described in the text or in a flowchart/pseudocode format.

An algorithmic flow diagram illustrating the NARX modelling process would make the methodology clearer and more reproducible.

5. Writing and Structure

Some sections are overly long and descriptive. The Results section in particular should emphasize interpretation rather than repeating trends visible in the figures.

The conclusions could be strengthened by highlighting the originality of the contribution compared to existing literature, and by discussing potential limitations of the model more explicitly.

6. Literature Review

The literature review is broad but lacks critical comparison. The authors should better highlight how their approach differs from or improves upon prior studies, especially those already using machine learning for pandemic-related demand modelling.

7. Validation and Robustness

Model validation is limited. The paper reports training, validation, and testing R-values, but does not include robustness checks such as sensitivity analysis, cross-validation, or comparisons with baseline models (e.g., ARIMA, regression). These are necessary to justify the choice of NARX.

8. Policy Implications

Although the paper mentions recommendations, they remain general. Stronger policy-oriented insights are expected, such as concrete strategies for railway operators to adapt capacity, prioritize services, or design contingency timetables under different crisis scenarios.

Comments for author File: Comments.pdf

Author Response

Dear editor and reviewer,

We sincerely thank you to review team for the next insightful and constructive comments on this manuscript. The manuscript has been carefully revised according to the reviewer comments.

We look forward to hearing from you on the revised manuscript. In the remainder of this letter, we provide detailed answers to each of the comments.

 

 

Comments from the Reviewer:

 

Reviewer 1

This manuscript addresses the modelling and simulation of rail passenger transport demand in the Slovak Republic under crisis conditions, using COVID-19 as a case study. The research topic is relevant and has practical significance for transport resilience planning. The dataset is comprehensive, and the application of a NARX neural network framework is appropriate. However, in its current form, the paper requires significant revisions before it can be considered for publication.

Major Concerns and Suggestions

1. Mismatch between Title and Content

The title suggests that the study involves simulation of the railway system, yet the content focuses solely on passenger demand modelling using NARX networks. No actual railway system simulation (e.g., operational adjustments, timetable scenarios, capacity flow simulation) is presented. The title should be revised to better reflect the scope of the study.

• Thank you. We agree with this comment and have revised the title to better match the actual scope of the study. The new title is: “Modeling and Forecasting Passenger Rail Demand in Slovakia under Crisis Conditions with NARX Neural Networks.”

1. Figures

The resolution of many figures is too low, making them difficult to read. All figures should be redrawn or exported at publication-quality resolution.

• Thank you for the feedback. All figures have been re-exported at sufficient quality. The graphs have been redrawn to remain clear even when reduced in size, and all axis labels and legends have been adjusted to a larger font size to improve readability.

Sub-figures lack proper labeling (e.g., (a), (b), (c)), which complicates cross-referencing in the text. Please revise accordingly.

• Thank you for the comment. In our manuscript, all graphs are presented as separate figures rather than multi-panel images; therefore, they were not labeled with letters (a), (b), (c). However, we have checked and ensured that the numbering and references in the text are consistent and clearly indicate which figure is being cited.

1. Figure Analysis

The discussion of figures is largely descriptive. The paper lacks deeper interpretive analysis and summary of what each figure implies about system behavior. For example, Figures 9–18 present trends, but the authors provide only superficial comments. More critical comparisons, synthesis, and implications should be provided.

• Thank you for the valuable feedback. In the Results section, after presenting Figures 9–18, we added a paragraph that synthesizes and interprets the key findings, such as the differing demand decline dynamics under school, workplace, and leisure restrictions and their implications for capacity planning. In the Discussion section, we included a deeper comparison and summary of the practical consequences of these trends for railway operators. Following all revisions, the figures were renumbered accordingly.

1. Code and Methodological Transparency

The manuscript contains screenshots of MATLAB code that are not clear enough for readers to interpret. Screenshots are not acceptable for publication-quality presentation. Instead, the algorithm should be described in the text or in a flowchart/pseudocode format.

An algorithmic flow diagram illustrating the NARX modelling process would make the methodology clearer and more reproducible.

• Thank you for the feedback. We kept the code screenshots in the manuscript as a visual aid to help readers understand the context, but we complemented them with a clear textual description of the NARX model implementation, including the data processing steps, network configuration, and performance evaluation. For better clarity, we also added a schematic workflow diagram, enabling readers to follow the modelling process without needing access to the source code.

1. Writing and Structure

Some sections are overly long and descriptive. The Results section in particular should emphasize interpretation rather than repeating trends visible in the figures.

The conclusions could be strengthened by highlighting the originality of the contribution compared to existing literature, and by discussing potential limitations of the model more explicitly.

• Thank you for the suggestion. We have expanded the conclusion with a dedicated section clearly stating the originality of the study in the context of existing literature (a regional application of the NARX model with the integration of government measures into passenger rail demand forecasting in Slovakia). We also added a more detailed discussion of the model’s limitations (simplified coding of intervention intensity, absence of comparisons with simpler models, lack of sensitivity analysis) and provided recommendations for future research.

1. Literature Review

The literature review is broad but lacks critical comparison. The authors should better highlight how their approach differs from or improves upon prior studies, especially those already using machine learning for pandemic-related demand modelling.

• Thank you for the valuable comment. We have enhanced the Literature review section with a critical discussion that directly compares our approach with existing studies applying machine learning during the pandemic. We emphasized that, unlike most prior work, we employed a NARX neural network specifically tailored to railway transport and explicitly integrated government intervention indicators into the model — an aspect that previous studies addressed only marginally or not at all.

1. Validation and Robustness

Model validation is limited. The paper reports training, validation, and testing R-values, but does not include robustness checks such as sensitivity analysis, cross-validation, or comparisons with baseline models (e.g., ARIMA, regression). These are necessary to justify the choice of NARX.

• Thank you. We agree with this comment. In the Methods and Discussion sections, we have added an explanation that the current validation relied only on R and MSE, which is a limitation. We explicitly state the need to extend validation with cross-validation, sensitivity analysis, and comparisons with simpler baseline models (ARIMA, regression) to more firmly justify the choice of NARX. We plan to incorporate these steps in future work.

1. Policy Implications

Although the paper mentions recommendations, they remain general. Stronger policy-oriented insights are expected, such as concrete strategies for railway operators to adapt capacity, prioritize services, or design contingency timetables under different crisis scenarios.

• Thank you for the feedback. We have elaborated on the recommendations in the Conclusion section to provide concrete guidance for railway operators. We added proposals for multi-level capacity strategies (10–20% reduction for moderate and 30–40% for strict measures), prioritization of essential services, development of emergency timetables, as well as the need for dynamic demand monitoring and coordination with regional authorities when school and workplace policies change.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors present study on modelling the impact of COVID-19 restrictions on rail passenger demand in the Slovak Republic. The topic is of significant interest to the transportation research community, particularly in the context of building resilient systems. The application of a NARX neural network model to capture the non-linear relationships is a commendable approach. The data collection effort, particularly the acquisition of proprietary data from the national rail operator, is substantial and valuable. However, the manuscript requires revisions before it can be considered for publication. The primary concerns revolve around the justification of the methodological choices, the depth of the analysis, and the clarity of the contributions relative to the existing literature.

1. The paper states a goal to focus on a "regional perspective" as a key contribution. However, the analysis and results are overwhelmingly presented at the national level or by comparing nearly identical regional trends. The authors note that differences between regions were "relatively small" and that measures were mostly national, which contradicts the premise of a regional analysis.
2. Coding all complex, multi-faceted government restrictions into a single binary variable is a oversimplification that threatens the validity of the model. A measure moving from "no restrictions" to "masks required" is coded the same as a measure moving from "masks required" to "full lockdown." This loses crucial information on the intensity of the intervention. It is better to explore a more nuanced encoding scheme.
3. The authors correctly state that traditional models like ARIMA are unsuitable for this non-linear, shock-driven period. To demonstrate the superiority of the chosen NARX model, it is essential to compare its performance against a simpler baseline model. The high R-value on the training set and the drop in performance for validation sets suggest a risk of overfitting. A comparative analysis would solidify the claim that the NARX approach is necessary and optimal.
4. The validation of the model is limited to fit statistics (R, MSE). It is better to include scenario analysis or sensitivity analysis to show how sensitive the output is to changes in the input variables.
5. The literature review table is extensive but largely descriptive. After presenting the table, the authors should explicitly state the identified research gap that their study fills.
6. Figures 9-18 are numerous and repetitive, often showing the same trend across different measures. Consider consolidating these into a single, multi-panel figure or moving some to a supplementary document.
7. The recommendations proposed capacity reductions (10-40%) are seemingly derived from the descriptive analysis in Section 5.1, not from the NARX model itself. The link between the model's output and these specific, actionable recommendations should be made much clearer.

Author Response

Dear editor and reviewer,

We sincerely thank you to review team for the next insightful and constructive comments on this manuscript. The manuscript has been carefully revised according to the reviewer comments.

We look forward to hearing from you on the revised manuscript. In the remainder of this letter, we provide detailed answers to each of the comments.

 

 

Comments from the Reviewer:

 

Reviewer 2

The authors present study on modelling the impact of COVID-19 restrictions on rail passenger demand in the Slovak Republic. The topic is of significant interest to the transportation research community, particularly in the context of building resilient systems. The application of a NARX neural network model to capture the non-linear relationships is a commendable approach. The data collection effort, particularly the acquisition of proprietary data from the national rail operator, is substantial and valuable. However, the manuscript requires revisions before it can be considered for publication. The primary concerns revolve around the justification of the methodological choices, the depth of the analysis, and the clarity of the contributions relative to the existing literature.

1. The paper states a goal to focus on a "regional perspective" as a key contribution. However, the analysis and results are overwhelmingly presented at the national level or by comparing nearly identical regional trends. The authors note that differences between regions were "relatively small" and that measures were mostly national, which contradicts the premise of a regional analysis.

• Thank you. We have refined the aim of the article in the introduction to clarify that the study is primarily national in scope but offers potential for regional application. In section 5.2.1, we added an explanation of why regional differences were minimal (mainly due to the nationwide nature of the measures and the centralized railway network) and further elaborated on this topic in the Discussion

1. Coding all complex, multi-faceted government restrictions into a single binary variable is a oversimplification that threatens the validity of the model. A measure moving from "no restrictions" to "masks required" is coded the same as a measure moving from "masks required" to "full lockdown." This loses crucial information on the intensity of the intervention. It is better to explore a more nuanced encoding scheme.

• Thank you for your comment. In the Discussion section, we added a critical reflection on this limitation and, in the Conclusion, a recommendation for future work to implement more detailed or weighted coding of intervention intensity so that the model can better capture varying levels of government measures.

1. The authors correctly state that traditional models like ARIMA are unsuitable for this non-linear, shock-driven period. To demonstrate the superiority of the chosen NARX model, it is essential to compare its performance against a simpler baseline model. The high R-value on the training set and the drop in performance for validation sets suggest a risk of overfitting. A comparative analysis would solidify the claim that the NARX approach is necessary and optimal.

• Thank you. In the Discussion and Conclusion sections, we expanded our considerations on the need to include benchmarking with simpler time-series models (e.g., ARIMA, classical regression) and highlighted the risk of overfitting indicated by the gap between training and validation R values. We emphasized that this is a step planned for future research.

1. The validation of the model is limited to fit statistics (R, MSE). It is better to include scenario analysis or sensitivity analysis to show how sensitive the output is to changes in the input variables.

• Thank you very much. In the Discussion and Conclusion sections, we explicitly identified this limitation and added a recommendation to perform cross-validation, sensitivity analysis, and scenario analysis to strengthen the model’s robustness and its applicability under different input conditions.

1. The literature review table is extensive but largely descriptive. After presenting the table, the authors should explicitly state the identified research gap that their study fills.

• Thank you. After the literature review table in Section 2 (Literature Review), we added a paragraph that explicitly identifies the research gap — namely, the absence of railway transport demand modeling in the context of Central Europe with the integration of government intervention measures into neural networks — and clearly shows how this study addresses and fills that gap.

1. Figures 9-18 are numerous and repetitive, often showing the same trend across different measures. Consider consolidating these into a single, multi-panel figure or moving some to a supplementary document.

• Thank you for your comment. We kept the graphs as separate figures but added explanatory text in Section 5.1 to justify this choice — although they may appear similar at first glance, each represents a different category of measures and its specific impact on demand. We emphasized that aggregating them would obscure subtle but important differences between the interventions.

1. The recommendations proposed capacity reductions (10-40%) are seemingly derived from the descriptive analysis in Section 5.1, not from the NARX model itself. The link between the model's output and these specific, actionable recommendations should be made much clearer.

• Thank you. In the Discussion section, we added an explanation that these percentages are derived from NARX model scenarios under different levels of restrictions, not merely from descriptive trends. In the Conclusion, we included a short paragraph explicitly linking the predicted demand declines to the recommended ranges of capacity reduction.

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for the opportunity to review an interesting, relevant and timely article. Nevertheless, there are areas that need to be improved:
1. In the introduction, we recommend highlighting the difference with other scientific works, i.e. what is the gap and what will make the article unique.
2. Since there should be a clear methodology section, it may be appropriate to rename section 3 and add a little more methodology.
3. At the beginning of section 5, do not make a summary as a conclusion, but make a brief introduction to what will be done in that section.
4. More critical insights from the authors of the article in the analysis of the results.
5. It would be ideal if we could include comments in the discussion or analysis of the results on how things are in 2022-2025, whether something has improved, simplified or remained the same, i.e. what is the impact of the pandemic on the long-term perspective of passenger rail transport.
6. In the conclusions, emphasize the limitations of the study and indicate further directions for research.

Author Response

Dear editor and reviewer,

We sincerely thank you to review team for the next insightful and constructive comments on this manuscript. The manuscript has been carefully revised according to the reviewer comments.

We look forward to hearing from you on the revised manuscript. In the remainder of this letter, we provide detailed answers to each of the comments.

 

 

Comments from the Reviewer:

 

Reviewer 3

Thank you for the opportunity to review an interesting, relevant and timely article. Nevertheless, there are areas that need to be improved:

1. In the introduction, we recommend highlighting the difference with other scientific works, i.e. what is the gap and what will make the article unique.

• Thank you. We have added a clear statement of the research gap and the study’s contribution in the introduction. Specifically, we point out the absence of passenger rail demand modeling in the context of Slovakia that integrates government intervention measures and applies NARX neural networks, thereby extending the current state of knowledge.

1. Since there should be a clear methodology section, it may be appropriate to rename section 3 and add a little more methodology.

• Thank you for your comment. We renamed Chapter 3 to “Data and Research Methodology” and expanded its content. We described the data sources in more detail, including preprocessing steps (seasonality removal, normalization), the configuration of the NARX network architecture, and the procedure for training, validation, and testing.

2. At the beginning of section 5, do not make a summary as a conclusion, but make a brief introduction to what will be done in that section.

• Thank you. We revised the introduction of Chapter 5 by removing premature summaries and instead clearly stating the purpose of the section, to present the model results and interpret the impact of individual measures on passenger rail demand.

3. More critical insights from the authors of the article in the analysis of the results.

• The Discussion section was expanded with a critical assessment, where we included reflections on data limitations, the risk of model overfitting, the simplified coding of measures, and recommendations on how to address these limitations in future research.

4. It would be ideal if we could include comments in the discussion or analysis of the results on how things are in 2022-2025, whether something has improved, simplified or remained the same, i.e. what is the impact of the pandemic on the long-term perspective of passenger rail transport.

• Thank you for your comment. In the Discussion section, we addressed the post-pandemic developments (2022–2025). We assessed the recovery of demand, the lasting impact of hybrid work, changes in travel habits, and the digitalization of railway services in Slovakia, thereby expanding the perspective on the long-term consequences of the pandemic.
  In the conclusions, emphasize the limitations of the study and indicate further directions for research.
• Thank you. We expanded the Conclusion section with Limitations and Future Research. We explicitly state the data limitations (binary coding of interventions, analysis limited to a single crisis period, risk of model overfitting) and recommend future directions — more detailed coding of interventions, benchmarking with ARIMA and regression models, scenario and sensitivity analyses, and extension to multimodal transport.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors The authors have addressed all of my previous concerns thoroughly and satisfactorily. ​​I have no further questions or suggestions.​ I recommend accepting the manuscript for publication in its current form.