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Perimeter control in a mixed bimodal bathtub model

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  • Dantsuji, Takao
  • Takayama, Yuki
  • Fukuda, Daisuke

Abstract

Perimeter control involves monitoring network-wide traffic and regulating traffic inflow to alleviate hypercongestion. Implementation of transit priority with perimeter control measures, which allow transit into a controlled area without queuing at the perimeter boundary, is an effective strategy in bimodal transportation systems. However, travelers’ behavior changes in response to perimeter control strategies, such as shifts in their departure times and transportation modes, have not been fully investigated. Therefore, important questions remain, such as the use of transit during perimeter control with transit priority. This paper examines the travelers’ behavior changes in response to perimeter control with transit priority in a mixed bimodal transportation system with cars and flexible route transit (FRT) vehicles. We model departure time and transportation mode choices in such a transportation system with hypercongestion and discomfort in FRT (called the mixed bimodal bathtub model). Initially, we investigate the properties of dynamic user equilibrium without perimeter control. Then, we study the equilibrium patterns during perimeter control with transit priority. Unlike existing works, we find that the number of FRT passengers decreases with time toward the desired arrival time and that FRT may not be used around the peak of rush hour. Furthermore, transit priority may not be sufficient to promote the use of FRT, and additional incentive such as subsidy for lower fares may be required to encourage FRT use during perimeter control. Finally, we show that operating many FRT vehicles does not always decrease the equilibrium cost, even under perimeter control with transit priority.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:173:y:2023:i:c:p:267-291
    DOI: 10.1016/j.trb.2023.05.003
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    1. 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.
    2. Guo, Qiangqiang & Ban, Xuegang (Jeff), 2020. "Macroscopic fundamental diagram based perimeter control considering dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 136(C), pages 87-109.
    3. Ramezani, Mohsen & Haddad, Jack & Geroliminis, Nikolas, 2015. "Dynamics of heterogeneity in urban networks: aggregated traffic modeling and hierarchical control," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 1-19.
    4. de Palma, André & Lindsey, Robin & Monchambert, Guillaume, 2017. "The economics of crowding in rail transit," Journal of Urban Economics, Elsevier, vol. 101(C), pages 106-122.
    5. Basso, Leonardo J. & Feres, Fernando & Silva, Hugo E., 2019. "The efficiency of bus rapid transit (BRT) systems: A dynamic congestion approach," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 47-71.
    6. 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.
    7. Bao, Yue & Verhoef, Erik T. & Koster, Paul, 2021. "Leaving the tub: The nature and dynamics of hypercongestion in a bathtub model with a restricted downstream exit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    8. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-179, March.
    9. Haddad, Jack, 2017. "Optimal perimeter control synthesis for two urban regions with aggregate boundary queue dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 1-25.
    10. Yildirimoglu, Mehmet & Sirmatel, Isik Ilber & Geroliminis, Nikolas, 2018. "Hierarchical control of heterogeneous large-scale urban road networks via path assignment and regional route guidance," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 106-123.
    11. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    12. 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.
    13. Gonzales, Eric J. & Daganzo, Carlos F., 2013. "The evening commute with cars and transit: Duality results and user equilibrium for the combined morning and evening peaks," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 286-299.
    14. Takayama, Yuki & Kuwahara, Masao, 2017. "Bottleneck congestion and residential location of heterogeneous commuters," Journal of Urban Economics, Elsevier, vol. 100(C), pages 65-79.
    15. 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.
    16. 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.
    17. 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.
    18. Velaga, Nagendra R. & Beecroft, Mark & Nelson, John D. & Corsar, David & Edwards, Peter, 2012. "Transport poverty meets the digital divide: accessibility and connectivity in rural communities," Journal of Transport Geography, Elsevier, vol. 21(C), pages 102-112.
    19. Arnott, Richard & Buli, Joshua, 2018. "Solving for equilibrium in the basic bathtub model," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 150-175.
    20. Chen, Zhi & Wu, Wen-Xiang & Huang, Hai-Jun & Shang, Hua-Yan, 2022. "Modeling traffic dynamics in periphery-downtown urban networks combining Vickrey's theory with Macroscopic Fundamental Diagram: user equilibrium, system optimum, and cordon pricing," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 278-303.
    21. Gonzales, Eric J., 2015. "Coordinated pricing for cars and transit in cities with hypercongestion," Economics of Transportation, Elsevier, vol. 4(1), pages 64-81.
    22. 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.
    23. Xu, Shu-Xian & Liu, Ronghui & Liu, Tian-Liang & Huang, Hai-Jun, 2018. "Pareto-improving policies for an idealized two-zone city served by two congestible modes," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 876-891.
    24. Lamotte, Raphaël & Geroliminis, Nikolas, 2018. "The morning commute in urban areas with heterogeneous trip lengths," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 794-810.
    25. Fosgerau, Mogens & Small, Kenneth A., 2013. "Hypercongestion in downtown metropolis," Journal of Urban Economics, Elsevier, vol. 76(C), pages 122-134.
    26. 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.
    27. Chiabaut, Nicolas, 2015. "Evaluation of a multimodal urban arterial: The passenger macroscopic fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 410-420.
    28. Geroliminis, Nikolas, 2015. "Cruising-for-parking in congested cities with an MFD representation," Economics of Transportation, Elsevier, vol. 4(3), pages 156-165.
    29. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    30. 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.
    31. 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.
    32. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    33. 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.
    34. Takayama, Yuki, 2020. "Who gains and who loses from congestion pricing in a monocentric city with a bottleneck?," Economics of Transportation, Elsevier, vol. 24(C).
    35. Fosgerau, Mogens & Kim, Jinwon & Ranjan, Abhishek, 2018. "Vickrey meets Alonso: Commute scheduling and congestion in a monocentric city," Journal of Urban Economics, Elsevier, vol. 105(C), pages 40-53.
    36. Bartholdi, John J. & Eisenstein, Donald D., 2012. "A self-coördinating bus route to resist bus bunching," Transportation Research Part B: Methodological, Elsevier, vol. 46(4), pages 481-491.
    37. Jin, Wen-Long, 2020. "Generalized bathtub model of network trip flows," Transportation Research Part B: Methodological, Elsevier, vol. 136(C), pages 138-157.
    38. Wen-Xiang Wu & Hai-Jun Huang, 2014. "Equilibrium and Modal Split in a Competitive Highway/Transit System Under Different Road-use Pricing Strategies," Journal of Transport Economics and Policy, University of Bath, vol. 48(1), pages 153-169, January.
    39. Haddad, Jack & Shraiber, Arie, 2014. "Robust perimeter control design for an urban region," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 315-332.
    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. Daganzo, Carlos F. & Pilachowski, Josh, 2011. "Reducing bunching with bus-to-bus cooperation," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 267-277, January.
    42. 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.
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