The Road Network Design Problem for the Deployment of Automated Vehicles (RNDP-AVs): A Nonlinear Programming Mathematical Model

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript presents a theoretical approach to optimise a dedicated urban network for AVs while CVs and AVs coexist through an application to the town of Delft.

The manuscript is well written, the literature review is comprehensive enough. The mathematical approach is sound and rigorous, and the conclusions are supported by the results.

Author Response

Dear reviewer 1,

Thank you for your feedback and comments.

Reviewer 2 Report

Comments and Suggestions for Authors

The study aims to formulate a Non-Linear Programming (NLP) problem for designing AV subnetworks during the transition phase when traffic equilibrium varies due to AVs’ operational efficiency and changes in the occupant's value of travel time. Some comments:

1. The model assumes a constant mixed traffic efficiency coefficient for every road, which may not accurately reflect real-world conditions.

 

2. The study primarily focuses on the city of Delft and does not consider external demand. This could limit the generalizability of the findings to other urban contexts or more complex traffic systems.

 

3. The computational times for the different planning strategies (8 hours for IP, 4 hours for LTP, and 13 hours for HP) could be a limitation, especially for larger and more complex networks.

 

4. Dedication of road space, while new to CAV, has been extensively studied in other contexts before, e.g. allocation of public transport lanes. Drawing parallels and providing some discussion on this would be beneficial. e.g. see Haitao, H., Menendez, M., & Guler, S. I. (2018). Analytical evaluation of flexible-sharing strategies on multimodal arterials. Transportation Research Part A: Policy and Practice, 114, 364-379.

 

 

5. The study centers on three distinct strategies for planning AV subnetworks: Incremental Planning (IP), Long-Term Planning (LTP), and Hybrid Planning (HP). Concentrating on a limited set of strategies might introduce bias into the research. The outcomes and conclusions drawn are largely dependent on the chosen methodologies. This potentially oversimplifies the complex challenges associated with AV integration.

Comments on the Quality of English Language

N.A.

Author Response

Dear Reviewer 2,

Thank you for your feedback. I will answer to your comments accordingly:

1. The model assumes a constant mixed traffic efficiency coefficient for every road, which may not accurately reflect real-world conditions.
2. The study primarily focuses on the city of Delft and does not consider external demand. This could limit the generalizability of the findings to other urban contexts or more complex traffic systems.
3. The computational times for the different planning strategies (8 hours for IP, 4 hours for LTP, and 13 hours for HP) could be a limitation, especially for larger and more complex networks.

 Thanks for the comments. All suggestions have been added as limitations and are highlighted in the final section, (lines 601-614):

The application of the RNDP-AVs model points towards a need of designing a subnetwork for AVs. This model was formulated with the introduction of some simplifications and assumptions, as stated in section 3. These simplifications and assumptions resulting in both limitations and future work opportunities. As limitations of model, proper of any academic exercise, we have for example, a constant mixed traffic efficiency coefficient and a constant road investment per kilometre. Furthermore, the application of the model has only been tested in city of Delft, and does not consider external demand, because of data availability and the assumed focus on the inner city traffic.

As future work, an extended model joining the decision on AV subnetworks with the time lag decision. Similarly, an improved model joining together the decision AV subnetworks and strategic location problem for V2I communication sites (5 km of radius), as well with traffic efficiency parameters more accurate, perhaps could be solved through heuristic methods [39,40], though more computationally costly to solve and the optimal solution might not be guaranteed. The same is true for other applications in bigger cities or larger networks. Another relevant improvement could be taking public transport as another alternative mode of transport, but it would involve both routes and schedules, transforming this road network design problem into a tricky combinatorial transit assignment problem [41]. Moreover, it is also possible to evolve to bi-level optimization and add improvements such as other cost components involving pollution, noise reduction, or other benefits, for example, freeing space in the city centre (e.g., parking and gas stations).

 

4. Dedication of road space, while new to CAV, has been extensively studied in other contexts before, e.g. allocation of public transport lanes. Drawing parallels and providing some discussion on this would be beneficial. e.g. see Haitao, H., Menendez, M., & Guler, S. I. (2018). Analytical evaluation of flexible-sharing strategies on multimodal arterials. Transportation Research Part A: Policy and Practice, 114, 364-379.

  Thanks for your suggestion. Supporting literature has been added in the discussion in section 1, line (69):

However, dedicated lanes encompass numerous practical challenges, and its implementation might not be easy. Nowadays, for example, bus and taxis dedicated lanes experience unauthorised circulation and illicit parking of human-driven vehicles – the so-called conventional vehicles (CVs). In this paper we are testing the scenario where, at some point, the deployment of AVs will happen in dedicated road infrastructure, with AV subnetworks to deploy the first driverless vehicles, i.e., AVs level 4 – a specific level of automation in which a vehicle drives automatically under certain conditions [7,8]. Restricted driving areas are not a novel practice, for instance, currently many urban centres ban the circulation of old vehicles to reduce air pollution. Legal aspects are involved, and traffic control in city centres might still be needed for pedestrians and bikes. In fact, from city authorities and other stakeholders’ perspectives, AV subnetworks will allow better traffic control, managing safety aspects and improving efficiency on network elements such as traffic intersections. From AV private owners’ perspective, AV subnetworks could be appreciated for convenience and comfort, which could potentially motivate buying such vehicles. Though, from the CV owners’ perspective, AV subnetworks could be unwelcome if they represent fewer route options, destinations hindrance and extra travel times.

 

5. The study centers on three distinct strategies for planning AV subnetworks: Incremental Planning (IP), Long-Term Planning (LTP), and Hybrid Planning (HP). Concentrating on a limited set of strategies might introduce bias into the research. The outcomes and conclusions drawn are largely dependent on the chosen methodologies. This potentially oversimplifies the complex challenges associated with AV integration.

Such limitations have been highlighted in the conclusions section (lines 601-614). However, we would not call the planning strategy a methodology. The strategies come from the context of the problem which is not eminently operational. You are not able to plan a whole network and build it all at once, therefore you have to have different planning horizons or intervals.

Reviewer 3 Report

Comments and Suggestions for Authors

P 2. Lines. 45-46. You claim that “We believe that, at some point, the deployment of AVs will happen in dedicated road infrastructure…et. c”. This needs some reasonable justification. This reviewer is of the opposite opinion. You must enlarge on this claim also giving some supporting references.

P4,  140-141You say “…links amongst the network have travel time functions that depend differently on each class” what do you mean “differently”. Re-write this sentence.

P4, l 195, replace “and O-D” with “an O-D”.

P8, The presentation of the 3 algorithms does not give any value to the reader and they are difficult to be understood. It is suggested to leave these, out. They can also be difficult to check.

 P12, Table 1. Put the “1” and “2” in the column titles “Congestion 1” and “Delay 2” in superscript.

P14, L406, concerning abbreviation IP, L409 concerning abbreviation LTP, L422 concerning abbreviation HP, put in parenthesis the whole wording (Incremental Planning) – Hybrid planning), etc- More generally it is suggested putting in, a Glossary of Terms.

P20, L454-455, what is the measure that increases by 10%?

 

 

Author Response

 

Dear Reviewer 3,

Thank you for your feedback. I will answer to your comments accordingly:

 

1. P 2. Lines. 45-46. You claim that “We believe that, at some point, the deployment of AVs will happen in dedicated road infrastructure…et. c”. This needs some reasonable justification. This reviewer is of the opposite opinion. You must enlarge on this claim also giving some supporting references.

  Thanks for your comment. We have clarified our stance. We do not wish to assume any future scenario as certain, but rather to test one particular case/scenario and explore its outcomes, (line 66). This scenario, despite being debatable, is one that many that researchers are putting forward as one of the options therefore it does deserve to be considered.

As automated vehicles (AVs) enter the scene, understanding their role in the future of mobility is a critical challenge to be faced all over the world [4]. A functional deployment is first envisioned of AVs gradually emerging over time with incompatibilities solved throughout this process [5]. Shladover [6] presented a functional deployment roadmap with some regions having Vehicle-to-Infrastructure (V2I) communication and other regions having separate dedicated lanes[6].

However, dedicated lanes encompass numerous practical challenges, and its implementation might not be easy. Nowadays, for example, bus and taxis dedicated lanes experience unauthorised circulation and illicit parking of human-driven vehicles – the so-called conventional vehicles (CVs). In this paper, we are testing the scenario where, at some point, the deployment of AVs will happen in dedicated road infrastructure, with AV subnetworks to deploy the first driverless vehicles, i.e., AVs level 4 – a specific level of automation in which a vehicle drives automatically under certain conditions [7,8]. Restricted driving areas are not a novel practice, for instance, currently many urban centres ban the circulation of old vehicles to reduce air pollution. Legal aspects are involved, and traffic control in city centres might still be needed for pedestrians and bikes. In fact, from city authorities and other stakeholders’ perspectives, AV subnetworks will allow better traffic control, managing safety aspects and improving efficiency on network elements such as traffic intersections. From AV private owners’ perspective, AV subnetworks could be appreciated for convenience and comfort, which could potentially motivate buying such vehicles. Though, from the CV owners’ perspective, AV subnetworks could be unwelcome if they represent fewer route options, destinations hindrance and extra travel times.

 

2. P4,  140-141You say “…links amongst the network have travel time functions that depend differently on each class” what do you mean “differently”. Re-write this sentence.

Thanks for your comment. We have rewritten the sentence (line 168), as its meaning was lost due to poor English.

This RNDP, with considering AVs and CVs in the same model, originates a multi-class traffic assignment – found in the literature [26–28]. Nevertheless, a multiclass traffic assignment can easily turn into an asymmetric assignment that naturally arises from each class differences [29–31]. Problems concerning the multi-class traffic assignment are resumed in two types of incoherence: behavioural or mathematical [32]. The behavioural incoherence happens if each class holds an individual travel time function or if links amongst the network have travel time functions differently depending on each class. To reduce the complexity while assuring convexity, a new variable is defined in this paper that aggregates the classes, so that AVs and CVs share a common link travel time function. This variable (total flow) embeds an added automated traffic efficiency. However, in some situations, a mathematical incoherence might appear because of the dependencies in the singular Jacobian matrix that implies a linear relationship between each class cost function and the weights used in the single flow variable grouping the classes [32]. In other words, mathematical incoherence happens when each class is distinguished by different costs (e.g., toll pricing or value of travel time). In this study, we calculated the effects of such linearity and we have concluded that such relationship resembles recent findings on AVs reduced value of travel time [33–35] – therefore, we accept the incoherence. This will be explained in the model section.

 

3. P4, l 195, replace “and O-D” with “an O-D”.

Thanks for your comment, we have made such a change.

 

4. P8, The presentation of the 3 algorithms does not give any value to the reader and they are difficult to be understood. It is suggested to leave these, out. They can also be difficult to check.

For transparency purposes, we find it essential to keep these tables 1-3. They are important to many readers.

 

5. P12, Table 1. Put the “1” and “2” in the column titles “Congestion 1” and “Delay 2” in superscript.

Due to the formatting, we are afraid that this cannot be done, as the table would not fit one page.

 

6. P14, L406, concerning abbreviation IP, L409 concerning abbreviation LTP, L422 concerning abbreviation HP, put in parenthesis the whole wording (Incremental Planning) – Hybrid planning), etc- More generally it is suggested putting in, a Glossary of Terms.

Thanks for your comment. We added the whole wording in the caption of the figures.

 

7. P20, L454-455, what is the measure that increases by 10%?

Thanks for your comment. We have rewritten the sentence (line 480-481).

Conversely, total travel time might increase to AVs (Figure 9) in the following situations:

• As AVs value of travel time decreases, AV passengers might travel longer which can be depicted by an increase in AVs delay while in congestion (see Figure 13). This occurs, for instance, at the penetration rate of 25%.
• AV trips might occur in shorter routes (lower distances) and experience higher travel times (Figure 11) This happens if AV subnetworks include roads with lower capacity/speed, when both AV delay and distance decrease. For example, this happens at a penetration rate of 10% in the IP and HP, and of 50% in the LTP.

 

 

 

 

Reviewer 4 Report

Comments and Suggestions for Authors

the paper evaluates the decision of which roads to dedicate to automated traffic with three planning strategies, in addition, or as a possible development the methodologies used in the following can be considered:

(Can you improve references with the following papers)

Electric vehicles charging infrastructure location: a genetic algorithm approach Efthymiou, D., Chrysostomou, K., Morfoulaki, M., Aifantopoulou, G.

Dynamic model for the EV's Charging Infrastructure Planning through Finite Element Method

Brenna M., Lazaroiu GC; Roscia M., Saadatmandi S.

 

 

Two-Stage Optimal Scheduling Strategy for Large-Scale Electric Vehicles Wang, X., Sun, C., Wang, R., Wei, T.    

 

 

datmandi S.aroiu G.C.

•  

Author Response

Dear Reviewer 4,

Thanks for your suggestions. However, the scope of this paper involves automated vehicles and the possible dedication of infrastructure (roads/links) to this new class of private vehicles that could involve a more efficient traffic behaviour (in terms of capacity) than the conventional/traditional human-driven vehicles. The first two papers that the reviewer suggested involve a location problem for charging infrastructure (points/nodes), in two interesting methodologies (genetic algorithm and finite elements). The third paper is also focused on scheduling operational problem for electric vehicles, which is also on another scope of this paper. All could serve as references for future work and thus they were added as reference in the conclusions section.

As future work, an extended model joining the decision on AV subnetworks with the time lag decision. Similarly, an improved model joining together the decision AV subnetworks and strategic location problem for V2I communication sites (5 km of radius), as well with traffic efficiency parameters more accurate, perhaps could be solved through heuristic methods [39,40], though more computationally costly to solve and the optimal solution might not be guaranteed. The same is true for other applications in bigger cities or larger networks. Another relevant improvement could be taking public transport as another alternative mode of transport, but it would involve both routes and schedules, transforming this road network design problem into a tricky combinatorial transit assignment problem [41]. Moreover, it is also possible to evolve to bi-level optimization and add improvements such as other cost components involving pollution, noise reduction, or other benefits, for example, freeing space in the city centre (e.g., parking and gas stations).

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

N.A.

Comments on the Quality of English Language

N.A.