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Primal Method for Determining the Most Likely Route Flows in Large Road Networks

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  • Hillel Bar-Gera

    (Department of Industrial Engineering and Management, Ben-Gurion University, P.O.B. 653, Be’er-Sheva 84105, Israel)

Abstract

This paper presents a method to identify the set of routes and their flows in a user-equilibrium traffic assignment solution. We present a general consistency condition that is satisfied by any set of minimum-cost routes, and show how it can be used in choosing a set of routes that is likely to be similar to the set of user-equilibrium routes. The proposed consistency condition is also essential for finding the entropy-maximizing route flows solution, which may be regarded as the most likely one. An efficient method for finding the entropy-maximizing solution is presented. Numerical results on several networks, including one of large scale, demonstrate the effectiveness of the proposed method. In most cases the method achieves a duality gap of practically zero in a short computation time.

Suggested Citation

  • Hillel Bar-Gera, 2006. "Primal Method for Determining the Most Likely Route Flows in Large Road Networks," Transportation Science, INFORMS, vol. 40(3), pages 269-286, August.
    • Handle: RePEc:inm:ortrsc:v:40:y:2006:i:3:p:269-286
    DOI: 10.1287/trsc.1050.0142
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    References listed on IDEAS

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    1. Harris, Britton, 2002. "Multiple paths through a network," ERSA conference papers ersa02p138, European Regional Science Association.
    2. Boyce David & Xiong Qian, 2004. "User-Optimal and System-Optimal Route Choices for a Large Road Network," Review of Network Economics, De Gruyter, vol. 3(4), pages 1-10, December.
    3. Janson, Bruce N., 1993. "Most likely origin-destination link uses from equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 27(5), pages 333-350, October.
    4. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
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    Cited by:

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    3. Xie, Chi, 2016. "New insights and improvements of using paired alternative segments for traffic assignmentAuthor-Name: Xie, Jun," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 406-424.
    4. Jiayang Li & Qianni Wang & Liyang Feng & Jun Xie & Yu Marco Nie, 2024. "A Day-to-Day Dynamical Approach to the Most Likely User Equilibrium Problem," Papers 2401.08013, arXiv.org.
    5. Wen-yi Zhang & Wei Guan & Ji-hui Ma & Jun-fang Tian, 2015. "A Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary Game," Networks and Spatial Economics, Springer, vol. 15(4), pages 1075-1092, December.
    6. Bar-Gera, Hillel, 2010. "Traffic assignment by paired alternative segments," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1022-1046, September.
    7. Rinaldi, Marco & Tampère, Chris M.J. & Viti, Francesco, 2018. "On characterizing the relationship between route choice behaviour and optimal traffic control solution space," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 892-906.
    8. Jafari, Ehsan & Pandey, Venktesh & Boyles, Stephen D., 2017. "A decomposition approach to the static traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 270-296.
    9. Marc Gaudry & Emile Quinet, 2012. "Shannon's measure of information, path averages and the origins of random utility models in transport itinerary or mode choice analysis," PSE Working Papers halshs-00713168, HAL.
    10. Florian, Michael & Morosan, Calin D., 2014. "On uniqueness and proportionality in multi-class equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 173-185.
    11. Boyce, David, 2007. "Future research on urban transportation network modeling," Regional Science and Urban Economics, Elsevier, vol. 37(4), pages 472-481, July.
    12. Marc Gaudry & Emile Quinet, 2012. "Shannon's measure of information, path averages and the origins of random utility models in transport itinerary or mode choice analysis," Working Papers halshs-00713168, HAL.
    13. Lu, Shu & (Marco) Nie, Yu, 2010. "Stability of user-equilibrium route flow solutions for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 609-617, May.
    14. Prateek Bansal & Rohan Shah & Stephen D. Boyles, 2018. "Robust network pricing and system optimization under combined long-term stochasticity and elasticity of travel demand," Transportation, Springer, vol. 45(5), pages 1389-1418, September.
    15. He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2010. "A link-based day-to-day traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 597-608, May.
    16. Bar-Gera, Hillel & Boyce, David & Nie, Yu (Marco), 2012. "User-equilibrium route flows and the condition of proportionality," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 440-462.
    17. Kumar, Amit & Peeta, Srinivas, 2015. "Entropy weighted average method for the determination of a single representative path flow solution for the static user equilibrium traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 213-229.
    18. Borchers, Marlies & Breeuwsma, Paul & Kern, Walter & Slootbeek, Jaap & Still, Georg & Tibben, Wouter, 2015. "Traffic user equilibrium and proportionality," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 149-160.
    19. O'Hare, Steven J. & Connors, Richard D. & Watling, David P., 2016. "Mechanisms that govern how the Price of Anarchy varies with travel demand," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 55-80.
    20. Louis Grange & Felipe González & Shlomo Bekhor, 2017. "Path Flow and Trip Matrix Estimation Using Link Flow Density," Networks and Spatial Economics, Springer, vol. 17(1), pages 173-195, March.
    21. Eikenbroek, Oskar A.L. & Still, Georg J. & van Berkum, Eric C. & Kern, Walter, 2018. "The Boundedly Rational User Equilibrium: A parametric analysis with application to the Network Design Problem," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 1-17.
    22. Jun Xie & Yu (Marco) Nie, 2019. "A New Algorithm for Achieving Proportionality in User Equilibrium Traffic Assignment," Transportation Science, INFORMS, vol. 53(2), pages 566-584, March.
    23. Jafari, Ehsan & Boyles, Stephen D., 2016. "Improved bush-based methods for network contraction," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 298-313.
    24. Xie, Chi & Kockelman, Kara M. & Waller, S. Travis, 2011. "A maximum entropy-least squares estimator for elastic origin–destination trip matrix estimation," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1465-1482.
    25. Li, Tao & Wan, Yan, 2019. "Estimating the geographic distribution of originating air travel demand using a bi-level optimization model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 267-291.

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