Highway Travel-Time Forecasting with Greenshields Model-Based Cascaded Fuzzy Logic Systems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper deals with a motorway travel time forecasting system using the Greenshields model and cascaded fuzzy logic systems. Although it addresses the topic of intelligent transport systems (ITS) and traffic data analysis, its main approach is theoretical-simulation and computer science. The contribution consists in developing a cascaded fuzzy logic system based on the Greenshields model, which is an interesting approach, but not entirely innovative. Fuzzy logic has been previously used in the literature in the context of travel time prediction. The paper can be considered to contribute new knowledge, but it is rather an incremental innovation than a breakthrough. However, the authors do not clearly identify the research gap in the introduction. Despite the literature review, it has not been clearly demonstrated why the proposed method is a significant step forward in the context of existing research. The contribution of the paper is of an engineering nature, but its advantages over previous approaches are not documented. The research goal has been clearly formulated, it is to develop and evaluate a cascade fuzzy logic system for predicting travel times on a motorway. The use of fuzzy logic based on the Greenshields model is well-motivated. The structure of the system has been described in detail, along with membership functions and inference rules. The structure of the article is clear, logical and well-organized. Individual sections develop the topic in a consistent manner.

The data analysis is in principle logical and coherent, but its statistical rigor could be greater. Comments in this regard that should be referred to in the text or justified:
1. The article does not contain an analysis of the sensitivity of the results to changes in input parameters (e.g. flow/density measurement errors). The uncertainty of prediction was also not taken into account - the travel times given are point times, without confidence intervals. There is no quantitative assessment of the error on the entire test set using standard metrics.

2. The choice of trapezoidal functions and the number of fuzz levels (e.g. 13 flow levels) seems arbitrary. No justification or comparative tests have been provided to show that such a split is optimal.

3. The comparison is limited to polynomial regression. There is no comparison with commonly used machine learning models, which significantly weakens the conclusion about the superiority of the fuzzy logic system.

4. The work assumes that the relations between flow, density and speed are stable over time. This is a serious simplification that does not take into account the dynamics of driver behavior or the impact of random events (e.g. accidents).

5. Only the Greenshields model was used, which is the simplest of the classic speed-density models. More advanced models, such as Greenberg's, Underwood's or Newell's, could provide a better representation for different scenarios.

6. No information is provided regarding the computational time, hardware resources or scalability of the proposed solution for a larger number of road sections or networks.

I also believe that the conclusions are too categorical and inadequate for the scale of the research (one test road section). What is missing is scientific humility and an indication of the limitations of the proposed approach.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors of the paper titled “Highway Travel Time Forecasting with Greenshields Model-Based Cascaded Fuzzy Logic Systems” present an innovative approach to predicting travel time on highways, based on Greenshields' theory and the application of cascaded fuzzy systems. The topic is current and relevant to the field of traffic engineering and intelligent transportation systems. The key innovation lies in localised modelling, whereby each road segment is treated as an individual fuzzy subsystem. This modular architecture enables the estimation of total travel time along traffic corridors to be updated dynamically. Unlike models that depend on training and large datasets, the proposed system uses rules derived from a physical traffic model, thus achieving transparency and straightforward application in real ITS environments.

The fuzzy rule base presented in the paper is constructed based on the theoretical relationships defined by the Greenshields model. In this model, the authors used predefined linguistic categories to represent traffic flow, density and vehicle speed. The rules are formulated in the classical 'if–then' format and derive from known functional relationships among key traffic parameters. It is important to emphasise that the rules are entirely static and manually defined, rather than being the result of algorithmic learning from data. This renders the model less adaptable for use in dynamic, non-linear and unpredictable traffic scenarios.

The current comparisons of the model results are qualitative or visual, in the form of graphs, and lack numerical validation. To elevate the scientific rigour and practical value of the paper, the authors are recommended to introduce standard evaluation metrics such as RMSE (root mean square error), MAE (mean absolute error), MAPE (mean absolute percentage error) and/or R² (coefficient of determination). Including these indicators would allow the model’s accuracy to be assessed objectively and enable direct comparison with existing approaches in the literature. This addition should be incorporated into Section 4, where the simulation results are presented.

A major shortcoming of the paper is that the authors did not conduct a sensitivity analysis. In other words, they did not examine how the model responds to inaccurate inputs, such as sensor errors, data deficiencies and sudden changes in traffic conditions. Including such an analysis in the study would demonstrate the model's reliability under real ITS conditions, thereby increasing confidence in its practical applicability. It is recommended that the sensitivity analysis be conducted within Section 4.

Within Section 4, particularly in the discussion section, the authors should also compare the results of the proposed model with those of other approaches from the literature. Including a comparison with models based on artificial intelligence (AI) methods applied under similar traffic conditions would be especially useful.

At the end of the conclusion, the authors should define possible directions for future research.

Technical note: In the submitted PDF, the text in Figures 17–26 is illegible.

The references are relevant and up to date.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

the authors responded constructively to all my comments and proposed specific changes to the text for each of them, I have no reason to oppose publication and I recommend the article for publication

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have considered all comments from the previous review stage and made appropriate revisions to the manuscript. Where direct changes were not feasible, they have provided clear and well-reasoned explanations. I recommend accepting the manuscript for publication in its current form.