Does Density Foster Shorter Public Transport Networks? A Network Expansion Simulation Approach

Round 1

Reviewer 1 Report

Greetings to Dear Authors!
Your article seemed interesting to me, but not sufficiently developed.

It seemed to me that you are embedding in your algorithm for building a model transport network a metric that calculates the coefficient of transport connectivity based on population density, and then conclude that these parameters are related. This seems like an under-explored idea of your research.

I couldn't figure out how you get an estimate of the population density at that point for your map point. Perhaps because of this, I have the feeling described above.

Comments:

- Please note that Figure 1 is misleading. First of all, it does not have the shortest path drawn on it. It's strange, why do you take the average path and how do you calculate the maximum/minimum paths in this case?

- Secondly, at Figure 1 you have a different network structure than the one you show at Figure 3 below. According to Figure 3, the trajectory is expected to be slightly different.

- By expanding the route map, you get an estimate of the new route for maximizing parameters. Nowhere do you say what happens if you get several estimated potential new routes. Suppose you take only the first value for the extension. In this case, the result may not be rigidly determined, that is, it requires any averaging/control. This seems to require a broader explanation.

The material that You present in article, in its current form, is difficult to repeat (I don't understand how) to an independent group of researchers. That is, you can't double-check the results.

Author Response

Greetings to Dear Authors!
Your article seemed interesting to me, but not sufficiently developed.

It seemed to me that you are embedding in your algorithm for building a model transport network a metric that calculates the coefficient of transport connectivity based on population density, and then conclude that these parameters are related. This seems like an under-explored idea of your research.

I couldn't figure out how you get an estimate of the population density at that point for your map point. Perhaps because of this, I have the feeling described above.

The algorithm keeps allocating additional transport links until x% of the population is connected (see last lines of Section 2, just before Section 3). According to the results in Figure 7, the precise definition of that x% is not very important as long as the x% > ~25%. Of course the spatial distribution of population plays a crucial role in this exercise. We use GHSL population grids. This has been made much clearer now in Section 2.1. Where we first introduce population weighted densities we refer to the key paper on that measure by Morton – we believe it is sufficiently well-specified by Morton so that we do not need to repeat it here.

Comments:

- Please note that Figure 1 is misleading. First of all, it does not have the shortest path drawn on it. It's strange, why do you take the average path and how do you calculate the maximum/minimum paths in this case?

- Secondly, at Figure 1 you have a different network structure than the one you show at Figure 3 below. According to Figure 3, the trajectory is expected to be slightly different.

Clearly the purpose of Figure 1 is insufficiently clear – it is meant to present key concepts graphically, not show outcomes of the modelling process per se. The caption has been revised, it now reads: “Graphical representation of key methodological terms that are used in this paper. Nodes are given as circles. Selected termini are filled black circles. Intermediate nodes are circles filled gray. A single connection (left, dashed arrow) is repeatedly selected from an OD matrix for a travel time improvement. This connection does not have a spatial form. A single path (middle, thick line) is sought between the connection points through an optimization routine. Such a path comprises multiple links (right, arrows) between intermediate and termini nodes. The links that comprise the selected path are indicated by thicker arrows, they receive a travel cost improvement vis-à-vis links that have not been selected.”

- By expanding the route map, you get an estimate of the new route for maximizing parameters. Nowhere do you say what happens if you get several estimated potential new routes. Suppose you take only the first value for the extension. In this case, the result may not be rigidly determined, that is, it requires any averaging/control. This seems to require a broader explanation.

This may have been insufficiently clear in the procedure. We have now emphasized in section 2.3 that “Subsequently only one path is selected that, within a specific maximum distance, meets the highest proxied return on investment. Thus, only the links comprising one path are se-lected for a speed upgrade in every model iteration.”

The material that You present in article, in its current form, is difficult to repeat (I don't understand how) to an independent group of researchers. That is, you can't double-check the results.

Fair point! We are trying to get our results and model publicly so all procedures can be verified and repeated. The code and results are currently available through an online repository: https://github.com/cjacobscrisioni/PublicTransportAllocator.git. We expect to have the results data on a repository with a fixed identifier early next week (written Fri 15/12/2023), and will need to replace the placeholder reference then.

Reviewer 2 Report

Author Response

The paper is devoted to the current issue of the relationship between transport planning and public transport. I rate the research algorithm very positively. I have no comments in terms of methodology, mathematical solution, generalization, etc. 

However, the algorithm does not take into account the possibility of limiting conditions in that somewhere it is not possible to ensure mobility and to design routes in some spatial areas due to restrictions. Restrictions may be due to legal conditions, private ownership, environmental impact limits (low-emission zones such as in Germany), etc. But the algorithm is theoretical. I recommend considering the limitations in further research and further publications. 

Thank you for your kind words. We of course acknowledge this limitation of our study and have made this more explicit in the Discussion section.

I recommend taking into account traffic congestion for further research on mobility, for example through the Braess paradox. 

Congestion is one of the aspects that we need to brush over here – but indeed 1) it may cause that system efficiency is not linear with network length; and 2) issues such as the Braess paradox may affect the assumption that link upgrades always decrease overall transport costs. This is noted now in the Discussion section as one of the (many) limitations of our approach.

I do not agree with the statement that the issue is rather new, because research in this area has been going on for decades, specifically at European universities, in the USA and Canada, in Russia and at universities in Southeast Asia and India. 

Agreed, and toned down in the introductory section of the paper

A walking speed of 4 km/h on average is optimistic and is realistic for a healthy part of the population. The rest of the population uses a lower speed, namely young children, the elderly, people with current health problems and people with disabilities. The average walking speed should therefore be lower, rather 3 km/h or 3.5 km/h is recommended. Lower values of average walking speed may limit the validity of the results using the algorithm and model. But the article is mathematical and theoretical, so the value of 4 km/h can remain. I recommend in further research to address walking speed for the entire spectrum of mobility participants. I do not even agree with the average speed of public transport of 30 km/h. This value is very different for different countries, for example in developed European cities it reaches significantly higher values. The value of public transport speed should be set according to the region. But this is enough for a theoretical article, I do not request a change.

These are fair points. We have emphasized the following in Section 2.1: “The chosen parameter values represent admittedly ad-hoc values that are not necessarily representative for the travel characteristics or the public transport systems in the studied cities. A limited sensitivity analysis has therefore been executed to explore the effects of the adopted settings. A later section will discuss this sensitivity analysis in more detail.”

I have comments on Annex C. The cities should have been ranked according to the number of inhabitants of the city agglomeration. 

This has been updated, thanks for the suggestion

I do not know the sources of data on the population of urban agglomerations. For example:  Dortmund-city in Germany has 0.7 M, with the whole agglomeration barely 5.8 M; Berlin-city in Germany has 3.7 M, with the whole agglomeration certainly more than 4.3 M. The authors must check the data on urban agglomerations. 

This is a fair point. We have clarified the sources for our population data in 2.1, and added the following:” It must be emphasized that the used population grids were created by disaggregating population census results over remotely sensed built-up fractions, so that they may deviate from official statistics.”

But the paper is of good quality, I recommend publishing it. I don't ask for corrections to be checked (second version), just a check from the editors.

Reviewer 3 Report

The authors try to construct a new algorithm to improve the transportation network expansion process. Several problems need to be solved before the acceptation.

1.     In the description of the model, the authors should emphasize the advantages of this new approach compared to previous ones. What gap does the new approach fill? The present version paid little attention on this explanation.

2.     For the explanation of the parameters, I suggest that the authors can summarize all these explanations in a table, either in the main text or in the appendix. It is difficult for the reader to find the meaning of all parameters in each formula, e.g. the parameters in Equation (7).

3.     The authors can construct some hypotheses based on the new simulation method, and then the part of results and discussions can test these hypotheses. Now it is difficult for the readers to understand whether this new method leads to new conclusions.

4.     Three independent variables in (10)-(12) are all about the population. Does the collinearity exist in these regressions? Are all the important variables included in these regressions? These regressions are close to a simple one-dimensional linear regression.

5.     The authors should extend the discussion part to include the explanations of the phenomenon in the regression results and policy suggestions. The present form is close to a simulation result report.

Author Response

The authors try to construct a new algorithm to improve the transportation network expansion process. Several problems need to be solved before the acceptation.

1. In the description of the model, the authors should emphasize the advantages of this new approach compared to previous ones. What gap does the new approach fill? The present version paid little attention on this explanation.

Thanks for this suggestion! Added the following: “The process is broadly similar to Yamins et al [29] in that iteratively only one pair is selected for an upgrade, and subsequently an optimal route is searched between the selected termini. Salient differences with Yamins et al are that in this paper 1) pairs are selected assuming that the investing agent aims at maximizing passenger kilometres travelled on the new link; 2) routes are sought that balance the additional returns from a detour versus the additional costs; and 3) the simulations are ran using granular, observed population distributions in multiple world cities.”

2. For the explanation of the parameters, I suggest that the authors can summarize all these explanations in a table, either in the main text or in the appendix. It is difficult for the reader to find the meaning of all parameters in each formula, e.g. the parameters in Equation (7).

This is a very good suggestion! Happy to share that this comment has been resolved proactively with the glossary in Appendix A.

2. The authors can construct some hypotheses based on the new simulation method, and then the part of results and discussions can test these hypotheses. Now it is difficult for the readers to understand whether this new method leads to new conclusions.

Added the following: “Whether denser land use can indeed foster proximate public transport availability is the topic of this paper. We expect that lower density cities would require a much more sizeable network (and hitherto investment) to supply proximate public transport to a size-able part of the population. Other explanations may be that cities need sufficient popula-tion mass to allow proximate public transport supply, or the effect of regional urban form, as the existence of a commuting zone or satellite suburbs may considerably affect the diffi-culty of providing proximate public transport.”

4. Three independent variables in (10)-(12) are all about the population. Does the collinearity exist in these regressions? Are all the important variables included in these regressions? These regressions are close to a simple one-dimensional linear regression.

Added the following text: Given the sizeable explained variance in all three regressions, we expect that the major explanatory factors are captured in these regressions. From pairwise correlations the variable have limited correlation (with a Pearson r-score below 0.41), except for  and , which do exhibit considerable correlation (0.76). Given that these variables do not seem to cause mutual inflated significance levels, we exclude problematic multicollinearity in our results.

5. The authors should extend the discussion part to include the explanations of the phenomenon in the regression results and policy suggestions. The present form is close to a simulation result report.

Thanks, fully agreed. The discussion section has been extended considerably to follow up on these suggestions.

Reviewer 4 Report

Author Response

Abastrct is too synthetic. It would be appropriate to better introduce the research and the scope of reference.

Abstract has been extended, hopefully sufficiently :)

The first paragraph, which introduces the topic covered, should be better explored, with a greater analysis of the state of the art. The references could also be further explored.

The introductory paragraphs are extended considerably, entailing a refined discussion of references (including some very recent).

The following paragraphs describe the methodology and the results but, overall, the paper is unbalanced as the final discussion is just a few lines.

Therefore, the entire text should be revised to try to homogenize the different phases of the research and, above all, the conclusions should be explored in depth.

Thanks for these suggestions! The Discussion section has been improved considerably following this suggestion. We think the current iteration provides a more balanced paper.

Round 2

Reviewer 3 Report

I suggest that the authors should still run a collinearity test, e.g. VIF test. Of course the present answers about the high R-square and t-test results can be viewed as the exclusion of collinearity.