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A Study on Network Design Problems for Multi-modal Networks by Probit-based Stochastic User Equilibrium

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  • Kenetsu Uchida
  • Agachai Sumalee
  • David Watling
  • Richard Connors

Abstract

This paper develops a multi-modal transport network model considering various travel modes including railway, bus, auto, and walking. Travellers are assumed to choose their multi-modal routes so as to minimise their perceived disutilities of travel following the Probit Stochastic User Equilibrium (SUE) condition. Factors influencing the disutility of a multi-modal route include actual travel times, discomfort on transit systems, expected waiting times, fares, and constants specific to transport modes. The paper then deals with the multi-modal network design problem (NDP). The paper employs the method of sensitivity analysis to define linear approximation functions between the Probit SUE link flows and the design parameters, which are then used as constraints in the sub-problem of the NDP instead of the original SUE condition. Based on this reformulated NDP, an efficient algorithm for solving the problem is proposed in the paper. Two instances of this general NDP formulation are then presented in the paper: the optimal frequency design problem for public transport services (FDP), and the anti-freezing admixture dispersion problem (AADP). Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Kenetsu Uchida & Agachai Sumalee & David Watling & Richard Connors, 2007. "A Study on Network Design Problems for Multi-modal Networks by Probit-based Stochastic User Equilibrium," Networks and Spatial Economics, Springer, vol. 7(3), pages 213-240, September.
    • Handle: RePEc:kap:netspa:v:7:y:2007:i:3:p:213-240
    DOI: 10.1007/s11067-006-9010-7
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    Cited by:

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    2. Elnaz Miandoabchi & Reza Farahani & W. Szeto, 2012. "Bi-objective bimodal urban road network design using hybrid metaheuristics," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(4), pages 583-621, December.
    3. Zhi-Chun Li & William Lam & S. Wong, 2012. "Optimization of Number of Operators and Allocation of New Lines in an Oligopolistic Transit Market," Networks and Spatial Economics, Springer, vol. 12(1), pages 1-20, March.
    4. David Eichler & Hillel Bar-Gera & Meir Blachman, 2013. "Vortex-Based Zero-Conflict Design of Urban Road Networks," Networks and Spatial Economics, Springer, vol. 13(3), pages 229-254, September.
    5. 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.
    6. 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.
    7. Paolo Delle Site, 2017. "On the Equivalence Between SUE and Fixed-Point States of Day-to-Day Assignment Processes with Serially-Correlated Route Choice," Networks and Spatial Economics, Springer, vol. 17(3), pages 935-962, September.
    8. Adriaan Hendrik van der Weijde & Vincent A.C. van den Berg, 2013. "Stochastic User Equilibrium Traffic Assignment with Price-sensitive Demand: Do Methods matter (much)?," Tinbergen Institute Discussion Papers 13-209/VIII, Tinbergen Institute.
    9. Dung-Ying Lin & Ampol Karoonsoontawong & S. Waller, 2011. "A Dantzig-Wolfe Decomposition Based Heuristic Scheme for Bi-level Dynamic Network Design Problem," Networks and Spatial Economics, Springer, vol. 11(1), pages 101-126, March.
    10. 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.
    11. Tao Zhang & Yang Yang & Gang Cheng & Minjie Jin, 2020. "A Practical Traffic Assignment Model for Multimodal Transport System Considering Low-Mobility Groups," Mathematics, MDPI, vol. 8(3), pages 1-19, March.
    12. Jing Zhao & Jie Yu & Xiaomei Xia & Jingru Ye & Yun Yuan, 2019. "Exclusive Bus Lane Network Design: A Perspective from Intersection Operational Dynamics," Networks and Spatial Economics, Springer, vol. 19(4), pages 1143-1171, December.
    13. Cervantes-Sanmiguel, K.I. & Chavez-Hernandez, M.V. & Ibarra-Rojas, O.J., 2023. "Analyzing the trade-off between minimizing travel times and reducing monetary costs for users in the transit network design," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 142-161.
    14. Inbal Haas & Shlomo Bekhor, 2017. "An Alternative Approach for Solving the Environmentally-Oriented Discrete Network Design Problem," Networks and Spatial Economics, Springer, vol. 17(3), pages 963-988, September.

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