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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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    1. Lo, Hong K. & Yip, C. W. & Wan, K. H., 2003. "Modeling transfer and non-linear fare structure in multi-modal network," Transportation Research Part B: Methodological, Elsevier, vol. 37(2), pages 149-170, February.
    2. 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.
    3. 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.
    4. Wagner A. Kamakura, 1989. "The Estimation of Multinomial Probit Models: A New Calibration Algorithm," Transportation Science, INFORMS, vol. 23(4), pages 253-265, November.
    5. 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.
    6. Carey, Malachy, 1994. "A model and strategy for train pathing with choice of lines, platforms, and routes," Transportation Research Part B: Methodological, Elsevier, vol. 28(5), pages 333-353, October.
    7. 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.
    8. Yang, Hai & Bell, Michael G. H., 1997. "Traffic restraint, road pricing and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 303-314, August.
    9. Carey, Malachy & Carville, Sinead, 2003. "Scheduling and platforming trains at busy complex stations," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(3), pages 195-224, March.
    10. Lam, W. H. K. & Gao, Z. Y. & Chan, K. S. & Yang, H., 1999. "A stochastic user equilibrium assignment model for congested transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 33(5), pages 351-368, June.
    11. Enrique Fernandez & Joaquin de Cea & Michael Florian & Enrique Cabrera, 1994. "Network Equilibrium Models with Combined Modes," Transportation Science, INFORMS, vol. 28(3), pages 182-192, August.
    12. Roger L. Tobin & Terry L. Friesz, 1988. "Sensitivity Analysis for Equilibrium Network Flow," Transportation Science, INFORMS, vol. 22(4), pages 242-250, November.
    13. Clark, Stephen D. & Watling, David P., 2002. "Sensitivity analysis of the probit-based stochastic user equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 36(7), pages 617-635, August.
    14. Abdulaal, Mustafa & LeBlanc, Larry J., 1979. "Continuous equilibrium network design models," Transportation Research Part B: Methodological, Elsevier, vol. 13(1), pages 19-32, March.
    15. Claude Chriqui & Pierre Robillard, 1975. "Common Bus Lines," Transportation Science, INFORMS, vol. 9(2), pages 115-121, May.
    16. Gao, Ziyou & Sun, Huijun & Shan, Lian Long, 2004. "A continuous equilibrium network design model and algorithm for transit systems," Transportation Research Part B: Methodological, Elsevier, vol. 38(3), pages 235-250, March.
    17. Roberto Cominetti & José Correa, 2001. "Common-Lines and Passenger Assignment in Congested Transit Networks," Transportation Science, INFORMS, vol. 35(3), pages 250-267, August.
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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    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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