IDEAS home Printed from https://ideas.repec.org/a/eee/transa/v156y2022icp113-132.html
   My bibliography  Save this article

Optimal pricing and investment in a multi-modal city — Introducing a macroscopic network design problem based on the MFD

Author

Listed:
  • Loder, Allister
  • Bliemer, Michiel C.J.
  • Axhausen, Kay W.

Abstract

Improving the performance of an existing transportation system is a challenge for engineers and policy makers as many dimensions and system design variables are interacting. In this paper, we propose the three-dimensional macroscopic fundamental diagram network design problem (3D-MFD-NDP). It is a strategic macroscopic tool to identify the directions of decision making in a multimodal transportation system, where the provision of roads and public transport services are interacting with costs for cars and public transport services in the performance of the entire road surface transportation system. The 3D-MFD-NDP models their effects aggregated at the network level and does not locate all measures to the road network. The objective function of the introduced 3D-MFD-NDP is minimizing the total travel time, while the design variables of the problem are the user costs for cars and bus tickets, the bus headway, the share of dedicated bus lanes and the length of the road network. The advantage of the 3D-MFD-NDP compared to existing approaches is that it is formulated as a mathematical program with equilibrium constraints (MPEC) that allows a fast closed-form solution instead of being simulation-based, usually computing many details not required in strategic decision making. We apply the 3D-MFD-NDP to the greater area of Zurich to study two different problems. First, we investigate how the current network performance can be increased by pricing and investment measures. Despite difficulties in identifying reliable cost information for the provision of roads, we find that substantial travel time savings are possible, especially when limiting car use by restricting its space and increasing its costs. Second, we investigate the response to a 20% population growth in urban and suburban regions with car and public transport prices as well as bus frequency as the free design variables. We find that the system can accommodate the population growth, but as the system costs are shared among more users, the costs per trip are lessened, which attenuates the steering effect of prices.

Suggested Citation

  • Loder, Allister & Bliemer, Michiel C.J. & Axhausen, Kay W., 2022. "Optimal pricing and investment in a multi-modal city — Introducing a macroscopic network design problem based on the MFD," Transportation Research Part A: Policy and Practice, Elsevier, vol. 156(C), pages 113-132.
    • Handle: RePEc:eee:transa:v:156:y:2022:i:c:p:113-132
    DOI: 10.1016/j.tra.2021.11.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096585642100313X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tra.2021.11.026?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ian W.H. Parry, 2009. "Pricing Urban Congestion," Annual Review of Resource Economics, Annual Reviews, vol. 1(1), pages 461-484, September.
    2. Ian W. H. Parry & Kenneth A. Small, 2009. "Should Urban Transit Subsidies Be Reduced?," American Economic Review, American Economic Association, vol. 99(3), pages 700-724, June.
    3. Alejandro Tirachini & David Hensher & Michiel Bliemer, 2014. "Accounting for travel time variability in the optimal pricing of cars and buses," Transportation, Springer, vol. 41(5), pages 947-971, September.
    4. S. F. A. Batista & Ludovic Leclercq, 2019. "Regional Dynamic Traffic Assignment Framework for Macroscopic Fundamental Diagram Multi-regions Models," Transportation Science, INFORMS, vol. 53(6), pages 1563-1590, November.
    5. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    6. Farahani, Reza Zanjirani & Miandoabchi, Elnaz & Szeto, W.Y. & Rashidi, Hannaneh, 2013. "A review of urban transportation network design problems," European Journal of Operational Research, Elsevier, vol. 229(2), pages 281-302.
    7. Tirachini, Alejandro & Hensher, David A. & Rose, John M., 2014. "Multimodal pricing and optimal design of urban public transport: The interplay between traffic congestion and bus crowding," Transportation Research Part B: Methodological, Elsevier, vol. 61(C), pages 33-54.
    8. Menendez, Monica & Daganzo, Carlos F., 2007. "Effects of HOV lanes on freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 41(8), pages 809-822, October.
    9. Dakic, Igor & Leclercq, Ludovic & Menendez, Monica, 2021. "On the optimization of the bus network design: An analytical approach based on the three-dimensional macroscopic fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 393-417.
    10. Rutherford, Thomas F., 1995. "Extension of GAMS for complementarity problems arising in applied economic analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 19(8), pages 1299-1324, November.
    11. Geroliminis, Nikolas & Daganzo, Carlos F., 2008. "Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 759-770, November.
    12. Takao Dantsuji & Daisuke Fukuda & Nan Zheng, 2021. "Simulation-based joint optimization framework for congestion mitigation in multimodal urban network: a macroscopic approach," Transportation, Springer, vol. 48(2), pages 673-697, April.
    13. Ji, Yuxuan & Geroliminis, Nikolas, 2012. "On the spatial partitioning of urban transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1639-1656.
    14. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    15. Nikolas Geroliminis & David M. Levinson, 2009. "Cordon Pricing Consistent with the Physics of Overcrowding," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 219-240, Springer.
    16. Loder, Allister & Dakic, Igor & Bressan, Lea & Ambühl, Lukas & Bliemer, Michiel C.J. & Menendez, Monica & Axhausen, Kay W., 2019. "Capturing network properties with a functional form for the multi-modal macroscopic fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 1-19.
    17. Guihaire, Valérie & Hao, Jin-Kao, 2008. "Transit network design and scheduling: A global review," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(10), pages 1251-1273, December.
    18. Batista, S.F.A. & Leclercq, Ludovic & Geroliminis, Nikolas, 2019. "Estimation of regional trip length distributions for the calibration of the aggregated network traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 192-217.
    19. Elnaz Miandoabchi & Reza Farahani & Wout Dullaert & W. Szeto, 2012. "Hybrid Evolutionary Metaheuristics for Concurrent Multi-Objective Design of Urban Road and Public Transit Networks," Networks and Spatial Economics, Springer, vol. 12(3), pages 441-480, September.
    20. Eric J. Gonzales & Nikolas Geroliminis & Michael J. Cassidy & Carlos F. Daganzo, 2010. "On the allocation of city space to multiple transport modes," Transportation Planning and Technology, Taylor & Francis Journals, vol. 33(8), pages 643-656, September.
    21. Daganzo, Carlos F., 2010. "Structure of competitive transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 434-446, May.
    22. Sun, Lijun & Tirachini, Alejandro & Axhausen, Kay W. & Erath, Alexander & Lee, Der-Horng, 2014. "Models of bus boarding and alighting dynamics," Transportation Research Part A: Policy and Practice, Elsevier, vol. 69(C), pages 447-460.
    23. Zheng, Nan & Waraich, Rashid A. & Axhausen, Kay W. & Geroliminis, Nikolas, 2012. "A dynamic cordon pricing scheme combining the Macroscopic Fundamental Diagram and an agent-based traffic model," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1291-1303.
    24. Kraus, Marvin, 2012. "Road pricing with optimal mass transit," Journal of Urban Economics, Elsevier, vol. 72(2), pages 81-86.
    25. Gonzales, Eric J. & Daganzo, Carlos F., 2012. "Morning commute with competing modes and distributed demand: User equilibrium, system optimum, and pricing," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1519-1534.
    26. Yildirimoglu, Mehmet & Geroliminis, Nikolas, 2014. "Approximating dynamic equilibrium conditions with macroscopic fundamental diagrams," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 186-200.
    27. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    28. Yang, Hai & Bell, Michael G. H., 1998. "A capacity paradox in network design and how to avoid it," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(7), pages 539-545, September.
    29. Ibarra-Rojas, O.J. & Delgado, F. & Giesen, R. & Muñoz, J.C., 2015. "Planning, operation, and control of bus transport systems: A literature review," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 38-75.
    30. Luathep, Paramet & Sumalee, Agachai & Lam, William H.K. & Li, Zhi-Chun & Lo, Hong K., 2011. "Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(5), pages 808-827, June.
    31. Wang, Shuaian & Meng, Qiang & Yang, Hai, 2013. "Global optimization methods for the discrete network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 42-60.
    32. Zheng, Nan & Geroliminis, Nikolas, 2013. "On the distribution of urban road space for multimodal congested networks," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 326-341.
    33. Daganzo, Carlos F. & Geroliminis, Nikolas, 2008. "An analytical approximation for the macroscopic fundamental diagram of urban traffic," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 771-781, November.
    34. Ceder, Avishai & Wilson, Nigel H. M., 1986. "Bus network design," Transportation Research Part B: Methodological, Elsevier, vol. 20(4), pages 331-344, August.
    35. Alex Anas & Robin Lindsey, 2011. "Reducing Urban Road Transportation Externalities: Road Pricing in Theory and in Practice," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 5(1), pages 66-88, Winter.
    36. Guler, S. Ilgin & Menendez, Monica, 2014. "Analytical formulation and empirical evaluation of pre-signals for bus priority," Transportation Research Part B: Methodological, Elsevier, vol. 64(C), pages 41-53.
    37. Daganzo, Carlos F & Geroliminis, Nikolas, 2008. "An analytical approximation for the macropscopic fundamental diagram of urban traffic," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4cb8h3jm, Institute of Transportation Studies, UC Berkeley.
    38. Mariotte, Guilhem & Leclercq, Ludovic & Laval, Jorge A., 2017. "Macroscopic urban dynamics: Analytical and numerical comparisons of existing models," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 245-267.
    39. Franz J. M. Salzborn, 1972. "Optimum Bus Scheduling," Transportation Science, INFORMS, vol. 6(2), pages 137-148, May.
    40. Zheng, Nan & Geroliminis, Nikolas, 2020. "Area-based equitable pricing strategies for multimodal urban networks with heterogeneous users," Transportation Research Part A: Policy and Practice, Elsevier, vol. 136(C), pages 357-374.
    41. Haddad, Jack & Geroliminis, Nikolas, 2012. "On the stability of traffic perimeter control in two-region urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 46(9), pages 1159-1176.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Schröder, Daniel & Kirn, Lukas & Kinigadner, Julia & Loder, Allister & Blum, Philipp & Xu, Yihan & Lienkamp, Markus, 2023. "Ending the myth of mobility at zero costs: An external cost analysis," Research in Transportation Economics, Elsevier, vol. 97(C).
    2. Xu, Guanhao & Gayah, Vikash V., 2023. "Non-unimodal and non-concave relationships in the network Macroscopic Fundamental Diagram caused by hierarchical streets," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 203-227.
    3. Chen, Yuanyi & Hu, Simon & Zheng, Yanchong & Xie, Shiwei & Hu, Qinru & Yang, Qiang, 2024. "Coordinated expansion planning of coupled power and transportation networks considering dynamic network equilibrium," Applied Energy, Elsevier, vol. 360(C).
    4. Schubert, Daniel & Sys, Christa & Vanelslander, Thierry & Roumboutsos, Athena, 2022. "No-queue road pricing: A comprehensive policy instrument for Europe?," Utilities Policy, Elsevier, vol. 78(C).
    5. Allister Loder & Fabienne Cantner & Lennart Adenaw & Nico Nachtigall & David Ziegler & Felix Gotzler & Markus B. Siewert & Stefan Wurster & Sebastian Goerg & Markus Lienkamp & Klaus Bogenberger, 2023. "Germany's nationwide travel experiment in 2022: public transport for 9 Euro per month -- First findings of an empirical study," Papers 2306.08297, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dantsuji, Takao & Takayama, Yuki & Fukuda, Daisuke, 2023. "Perimeter control in a mixed bimodal bathtub model," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 267-291.
    2. Amirgholy, Mahyar & Shahabi, Mehrdad & Gao, H. Oliver, 2017. "Optimal design of sustainable transit systems in congested urban networks: A macroscopic approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 261-285.
    3. Zheng, Nan & Geroliminis, Nikolas, 2013. "On the distribution of urban road space for multimodal congested networks," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 326-341.
    4. Amirgholy, Mahyar & Gao, H. Oliver, 2017. "Modeling the dynamics of congestion in large urban networks using the macroscopic fundamental diagram: User equilibrium, system optimum, and pricing strategies," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 215-237.
    5. Gao, Xueyu (Shirley) & Gayah, Vikash V., 2018. "An analytical framework to model uncertainty in urban network dynamics using Macroscopic Fundamental Diagrams," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 660-675.
    6. Dakic, Igor & Yang, Kaidi & Menendez, Monica & Chow, Joseph Y.J., 2021. "On the design of an optimal flexible bus dispatching system with modular bus units: Using the three-dimensional macroscopic fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 148(C), pages 38-59.
    7. Zheng, Nan & Geroliminis, Nikolas, 2020. "Area-based equitable pricing strategies for multimodal urban networks with heterogeneous users," Transportation Research Part A: Policy and Practice, Elsevier, vol. 136(C), pages 357-374.
    8. Liu, Wei & Geroliminis, Nikolas, 2016. "Modeling the morning commute for urban networks with cruising-for-parking: An MFD approach," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 470-494.
    9. Ampountolas, Konstantinos & Zheng, Nan & Geroliminis, Nikolas, 2017. "Macroscopic modelling and robust control of bi-modal multi-region urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 616-637.
    10. Loder, Allister & Dakic, Igor & Bressan, Lea & Ambühl, Lukas & Bliemer, Michiel C.J. & Menendez, Monica & Axhausen, Kay W., 2019. "Capturing network properties with a functional form for the multi-modal macroscopic fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 1-19.
    11. Anderson, Paul & Geroliminis, Nikolas, 2020. "Dynamic lane restrictions on congested arterials," Transportation Research Part A: Policy and Practice, Elsevier, vol. 135(C), pages 224-243.
    12. Lehe, Lewis J. & Pandey, Ayush, 2024. "A bathtub model of transit congestion," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    13. Fournier, Nicholas, 2021. "Hybrid pedestrian and transit priority zoning policies in an urban street network: Evaluating network traffic flow impacts with analytical approximation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 152(C), pages 254-274.
    14. Zhong, R.X. & Chen, C. & Huang, Y.P. & Sumalee, A. & Lam, W.H.K. & Xu, D.B., 2018. "Robust perimeter control for two urban regions with macroscopic fundamental diagrams: A control-Lyapunov function approach," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 687-707.
    15. Daganzo, Carlos F. & Lehe, Lewis J., 2015. "Distance-dependent congestion pricing for downtown zones," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 89-99.
    16. Daganzo, Carlos F & Lehe, Lewis J, 2014. "Distance-dependent Congestion Pricing for Downtown Zones," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt9vz1b9rs, Institute of Transportation Studies, UC Berkeley.
    17. Hörcher, Daniel & Tirachini, Alejandro, 2021. "A review of public transport economics," Economics of Transportation, Elsevier, vol. 25(C).
    18. Saeedmanesh, Mohammadreza & Geroliminis, Nikolas, 2017. "Dynamic clustering and propagation of congestion in heterogeneously congested urban traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 193-211.
    19. Gayah, Vikash V. & Gao, Xueyu (Shirley) & Nagle, Andrew S., 2014. "On the impacts of locally adaptive signal control on urban network stability and the Macroscopic Fundamental Diagram," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 255-268.
    20. Javier Durán-Micco & Pieter Vansteenwegen, 2022. "A survey on the transit network design and frequency setting problem," Public Transport, Springer, vol. 14(1), pages 155-190, March.

    More about this item

    Keywords

    Pricing; Investment; MFD; Congestion; Bus; MPEC;
    All these keywords.

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transa:v:156:y:2022:i:c:p:113-132. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/547/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.