IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v240y2015i1p98-108.html
   My bibliography  Save this article

Finding optimal hyperpaths in large transit networks with realistic headway distributions

Author

Listed:
  • Li, Qianfei
  • (Will) Chen, Peng
  • (Marco) Nie, Yu

Abstract

This paper implements and tests a label-setting algorithm for finding optimal hyperpaths in large transit networks with realistic headway distributions. It has been commonly assumed in the literature that headway is exponentially distributed. To validate this assumption, the empirical headway data archived by Chicago Transit Agency are fitted into various probabilistic distributions. The results suggest that the headway data fit much better with Loglogistic, Gamma and Erlang distributions than with the exponential distribution. Accordingly, we propose to model headway using the Erlang distribution in the proposed algorithm, because it best balances realism and tractability. When headway is not exponentially distributed, finding optimal hyperpaths may require enumerating all possible line combinations at each transfer stop, which is tractable only for a small number of alternative lines. To overcome this difficulty, a greedy method is implemented as a heuristic and compared to the brute-force enumeration method. The proposed algorithm is tested on a large scale CTA bus network that has over 10,000 stops. The results show that (1) the assumption of exponentially distributed headway may lead to sub-optimal route choices and (2) the heuristic greedy method provides near optimal solutions in all tested cases.

Suggested Citation

  • Li, Qianfei & (Will) Chen, Peng & (Marco) Nie, Yu, 2015. "Finding optimal hyperpaths in large transit networks with realistic headway distributions," European Journal of Operational Research, Elsevier, vol. 240(1), pages 98-108.
  • Handle: RePEc:eee:ejores:v:240:y:2015:i:1:p:98-108
    DOI: 10.1016/j.ejor.2014.06.046
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221714005499
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2014.06.046?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. Schmöcker, Jan-Dirk & Bell, Michael G.H. & Kurauchi, Fumitaka, 2008. "A quasi-dynamic capacity constrained frequency-based transit assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 925-945, December.
    2. Spiess, Heinz & Florian, Michael, 1989. "Optimal strategies: A new assignment model for transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 23(2), pages 83-102, April.
    3. Belgacem Bouzaïene-Ayari & Michel Gendreau & Sang Nguyen, 2001. "Modeling Bus Stops in Transit Networks: A Survey and New Formulations," Transportation Science, INFORMS, vol. 35(3), pages 304-321, August.
    4. Jia Hao Wu & Michael Florian & Patrice Marcotte, 1994. "Transit Equilibrium Assignment: A Model and Solution Algorithms," Transportation Science, INFORMS, vol. 28(3), pages 193-203, August.
    5. Schmöcker, Jan-Dirk & Fonzone, Achille & Shimamoto, Hiroshi & Kurauchi, Fumitaka & Bell, Michael G.H., 2011. "Frequency-based transit assignment considering seat capacities," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 392-408, February.
    6. Cepeda, M. & Cominetti, R. & Florian, M., 2006. "A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 40(6), pages 437-459, July.
    7. Jan-Dirk Schmöcker & Michael G.H. Bell & Fumitaka Kurauchi & Hiroshi Shimamoto, 2009. "A Game Theoretic Approach to the Determination of Hyperpaths in Transportation Networks," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 1-18, Springer.
    8. Joaquín de Cea & Enrique Fernández, 1993. "Transit Assignment for Congested Public Transport Systems: An Equilibrium Model," Transportation Science, INFORMS, vol. 27(2), pages 133-147, May.
    9. E. E. Osuna & G. F. Newell, 1972. "Control Strategies for an Idealized Public Transportation System," Transportation Science, INFORMS, vol. 6(1), pages 52-72, February.
    10. Claude Chriqui & Pierre Robillard, 1975. "Common Bus Lines," Transportation Science, INFORMS, vol. 9(2), pages 115-121, May.
    11. Roberto Cominetti & José Correa, 2001. "Common-Lines and Passenger Assignment in Congested Transit Networks," Transportation Science, INFORMS, vol. 35(3), pages 250-267, August.
    12. Guido Gentile & Sang Nguyen & Stefano Pallottino, 2005. "Route Choice on Transit Networks with Online Information at Stops," Transportation Science, INFORMS, vol. 39(3), pages 289-297, August.
    13. Nguyen, S. & Pallottino, S., 1988. "Equilibrium traffic assignment for large scale transit networks," European Journal of Operational Research, Elsevier, vol. 37(2), pages 176-186, November.
    14. Tong, C.O. & Wong, S.C., 1998. "A stochastic transit assignment model using a dynamic schedule-based network," Transportation Research Part B: Methodological, Elsevier, vol. 33(2), pages 107-121, April.
    15. Trozzi, Valentina & Gentile, Guido & Bell, Michael G.H. & Kaparias, Ioannis, 2013. "Dynamic user equilibrium in public transport networks with passenger congestion and hyperpaths," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 266-285.
    16. Volpentesta, Antonio P., 2008. "Hypernetworks in a directed hypergraph," European Journal of Operational Research, Elsevier, vol. 188(2), pages 390-405, July.
    17. Bell, Michael G.H. & Trozzi, Valentina & Hosseinloo, Solmaz Haji & Gentile, Guido & Fonzone, Achille, 2012. "Time-dependent Hyperstar algorithm for robust vehicle navigation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(5), pages 790-800.
    18. Sang Nguyen & Stefano Pallottino & Michel Gendreau, 1998. "Implicit Enumeration of Hyperpaths in a Logit Model for Transit Networks," Transportation Science, INFORMS, vol. 32(1), pages 54-64, February.
    19. Dial, Robert B., 1979. "A model and algorithm for multicriteria route-mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 311-316, December.
    20. Philippe H. J. Marguier & Avishai Ceder, 1984. "Passenger Waiting Strategies for Overlapping Bus Routes," Transportation Science, INFORMS, vol. 18(3), pages 207-230, August.
    21. Bell, Michael G.H., 2009. "Hyperstar: A multi-path Astar algorithm for risk averse vehicle navigation," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 97-107, January.
    22. Fitsum Teklu, 2008. "A Stochastic Process Approach for Frequency-based Transit Assignment with Strict Capacity Constraints," Networks and Spatial Economics, Springer, vol. 8(2), pages 225-240, September.
    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. Zhang, Yu & Tang, Jiafu, 2018. "A robust optimization approach for itinerary planning with deadline," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 113(C), pages 56-74.
    2. Xu, Zhandong & Xie, Jun & Liu, Xiaobo & Nie, Yu (Marco), 2020. "Hyperpath-based algorithms for the transit equilibrium assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    3. Luo, Qiang & Yuan, Jie & Chen, Xinqiang & Wu, Shubo & Qu, Zhijian & Tang, Jinjun, 2019. "Analyzing start-up time headway distribution characteristics at signalized intersections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    4. Chai, Huajun, 2019. "Dynamic Traffic Routing and Adaptive Signal Control in a Connected Vehicles Environment," Institute of Transportation Studies, Working Paper Series qt9ng3z8vn, Institute of Transportation Studies, UC Davis.
    5. Redmond, Michael & Campbell, Ann Melissa & Ehmke, Jan Fabian, 2022. "Reliability in public transit networks considering backup itineraries," European Journal of Operational Research, Elsevier, vol. 300(3), pages 852-864.
    6. Liu, Yang & Blandin, Sebastien & Samaranayake, Samitha, 2019. "Stochastic on-time arrival problem in transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 122-138.
    7. Zhang, Yu & Tang, Jiafu, 2018. "Itinerary planning with time budget for risk-averse travelers," European Journal of Operational Research, Elsevier, vol. 267(1), pages 288-303.
    8. Ren, Hualing & Song, Yingjie & Long, Jiancheng & Si, Bingfeng, 2021. "A new transit assignment model based on line and node strategies," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 121-142.
    9. Yunting Song & Nuo Wang, 2021. "On probability distributions of the time deviation law of container liner ships under interference uncertainty," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 354-367, January.

    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. Valentina Trozzi & Guido Gentile & Ioannis Kaparias & Michael Bell, 2015. "Effects of Countdown Displays in Public Transport Route Choice Under Severe Overcrowding," Networks and Spatial Economics, Springer, vol. 15(3), pages 823-842, September.
    2. Cortés, Cristián E. & Jara-Moroni, Pedro & Moreno, Eduardo & Pineda, Cristobal, 2013. "Stochastic transit equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 51(C), pages 29-44.
    3. Trozzi, Valentina & Gentile, Guido & Bell, Michael G.H. & Kaparias, Ioannis, 2013. "Dynamic user equilibrium in public transport networks with passenger congestion and hyperpaths," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 266-285.
    4. Padma Seetharaman, 2017. "Modelling risk aversion using a disaggregate stochastic process model in congested transit networks," Public Transport, Springer, vol. 9(3), pages 549-569, October.
    5. Jiang, Y. & Szeto, W.Y., 2016. "Reliability-based stochastic transit assignment: Formulations and capacity paradox," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 181-206.
    6. Codina, Esteve & Rosell, Francisca, 2017. "A heuristic method for a congested capacitated transit assignment model with strategies," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 293-320.
    7. Ren, Hualing & Song, Yingjie & Long, Jiancheng & Si, Bingfeng, 2021. "A new transit assignment model based on line and node strategies," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 121-142.
    8. Sun, S. & Szeto, W.Y., 2018. "Logit-based transit assignment: Approach-based formulation and paradox revisit," Transportation Research Part B: Methodological, Elsevier, vol. 112(C), pages 191-215.
    9. Xu, Zhandong & Xie, Jun & Liu, Xiaobo & Nie, Yu (Marco), 2020. "Hyperpath-based algorithms for the transit equilibrium assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    10. Nair, Rahul & Miller-Hooks, Elise, 2014. "Equilibrium network design of shared-vehicle systems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 47-61.
    11. Du, Muqing & Chen, Anthony, 2022. "Sensitivity analysis for transit equilibrium assignment and applications to uncertainty analysis," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 175-202.
    12. Tian, Qingyun & Wang, David Z.W. & Lin, Yun Hui, 2021. "Service operation design in a transit network with congested common lines," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 81-102.
    13. Khani, Alireza, 2019. "An online shortest path algorithm for reliable routing in schedule-based transit networks considering transfer failure probability," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 549-564.
    14. S. Mahmassani, Hani & F. Hyland, Michael, 2016. "Gap-based transit assignment algorithm with vehicle capacity constraints: Simulation-based implementation and large-scale applicationAuthor-Name: Verbas, Ömer," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 1-16.
    15. Wu, Di & Yin, Yafeng & Lawphongpanich, Siriphong, 2011. "Pareto-improving congestion pricing on multimodal transportation networks," European Journal of Operational Research, Elsevier, vol. 210(3), pages 660-669, May.
    16. Cortés, Cristián E. & Donoso, Pedro & Gutiérrez, Leonel & Herl, Daniel & Muñoz, Diego, 2023. "A recursive stochastic transit equilibrium model estimated using passive data from Santiago, Chile," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
    17. Cepeda, M. & Cominetti, R. & Florian, M., 2006. "A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 40(6), pages 437-459, July.
    18. Szeto, W.Y. & Jiang, Y., 2014. "Transit route and frequency design: Bi-level modeling and hybrid artificial bee colony algorithm approach," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 235-263.
    19. Canca, David & Andrade-Pineda, José Luis & De los Santos, Alicia & Calle, Marcos, 2018. "The Railway Rapid Transit frequency setting problem with speed-dependent operation costs," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 494-519.
    20. Tarun Rambha & Stephen D. Boyles & S. Travis Waller, 2016. "Adaptive Transit Routing in Stochastic Time-Dependent Networks," Transportation Science, INFORMS, vol. 50(3), pages 1043-1059, August.

    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:ejores:v:240:y:2015:i:1:p:98-108. 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/locate/eor .

    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.