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

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  • 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.

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  • 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
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    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Daganzo, Carlos F., 2010. "Structure of competitive transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 434-446, May.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Kraus, Marvin, 2012. "Road pricing with optimal mass transit," Journal of Urban Economics, Elsevier, vol. 72(2), pages 81-86.
    15. 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.
    16. 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.
    17. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. 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.
    27. 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.
    28. 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.
    29. Ceder, Avishai & Wilson, Nigel H. M., 1986. "Bus network design," Transportation Research Part B: Methodological, Elsevier, vol. 20(4), pages 331-344, August.
    30. 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.
    31. 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.
    32. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    33. 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.
    34. 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.
    35. 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.
    36. 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.
    37. 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.
    38. Franz J. M. Salzborn, 1972. "Optimum Bus Scheduling," Transportation Science, INFORMS, vol. 6(2), pages 137-148, May.
    39. 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.
    40. 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.
    41. 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.
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    Pricing; Investment; MFD; Congestion; Bus; MPEC;
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