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Solving network equilibrium problems on multimodal urban transportation networks with multiple user classes

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  • JOAQUÍN DE CEA
  • J. ENRIQUE FERNÁNDEZ
  • VALÉRIE DEKOCK
  • ALEXANDRA SOTO

Abstract

A modelling approach for solving quite general network equilibrium problems (with fixed trip productions and attractions) intrinsic to the urban transport planning process is presented. The framework can consider a variety of demand models and route choice behaviours within the same implementation, including multiple user classes and combined travel modes that interact on the same physical network. The demand choices are assumed to have a hierarchical structure. When trip distribution is variable, a doubly constrained entropy‐maximizing model is considered at the first level of choice and a hierarchical logit model is used for the remaining demand choices (time of departure, travel mode, transfer point for combined modes, etc.). If trip distribution is considered to be exogenous, the demand choices are modelled as a hierarchical logit. One of the main features of the model is that it considers the effects of congestion on the road network as well as congestion and capacity constraints effects in each public transport service network. The problem is formulated mathematically as a variational inequality, with asymmetric cost functions, and solved following the diagonalization procedure. Each iteration of the aforementioned procedure solves an optimization problem using the Evans algorithm. Sufficient conditions for the existence and uniqueness of the solution to the diagonalized problem are obtained. The main results of a simple example (solved with an academic version of the proposed algorithm) are presented to show the consistency of the equilibrium flows and levels of services obtained using the model. Finally, a real scale implementation of the model is briefly described to show the feasibility of its application.

Suggested Citation

  • Joaquín De Cea & J. Enrique Fernández & Valérie Dekock & Alexandra Soto, 2004. "Solving network equilibrium problems on multimodal urban transportation networks with multiple user classes," Transport Reviews, Taylor & Francis Journals, vol. 25(3), pages 293-317, January.
    • Handle: RePEc:taf:transr:v:25:y:2004:i:3:p:293-317
    DOI: 10.1080/0144164042000335805
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    1. 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.
    2. T. Abrahamsson & L. Lundqvist, 1999. "Formulation and Estimation of Combined Network Equilibrium Models with Applications to Stockholm," Transportation Science, INFORMS, vol. 33(1), pages 80-100, February.
    3. Michael Florian, 1977. "A Traffic Equilibrium Model of Travel by Car and Public Transit Modes," Transportation Science, INFORMS, vol. 11(2), pages 166-179, May.
    4. David Boyce & Hillel Bar–Gera, 2003. "Validation of Multiclass Urban Travel Forecasting Models Combining Origin–Destination, Mode, and Route Choices," Journal of Regional Science, Wiley Blackwell, vol. 43(3), pages 517-540, August.
    5. 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.
    6. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    7. Stella C. Dafermos, 1971. "An Extended Traffic Assignment Model with Applications to Two-Way Traffic," Transportation Science, INFORMS, vol. 5(4), pages 366-389, November.
    8. Caroline Fisk & Sang Nguyen, 1982. "Solution Algorithms for Network Equilibrium Models with Asymmetric User Costs," Transportation Science, INFORMS, vol. 16(3), pages 361-381, August.
    9. Stella Dafermos, 1982. "Relaxation Algorithms for the General Asymmetric Traffic Equilibrium Problem," Transportation Science, INFORMS, vol. 16(2), pages 231-240, May.
    10. Stella C. Dafermos, 1972. "The Traffic Assignment Problem for Multiclass-User Transportation Networks," Transportation Science, INFORMS, vol. 6(1), pages 73-87, February.
    11. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
    12. 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.
    13. Sang Nguyen & Clermont Dupuis, 1984. "An Efficient Method for Computing Traffic Equilibria in Networks with Asymmetric Transportation Costs," Transportation Science, INFORMS, vol. 18(2), pages 185-202, May.
    14. Bianchi, R. & Jara-Di­az, S. R. & de D. Ortúzar, J., 1998. "Modelling new pricing strategies for the Santiago Metro," Transport Policy, Elsevier, vol. 5(4), pages 223-232, October.
    15. Mustafa Abdulaal & Larry J. LeBlanc, 1979. "Methods for Combining Modal Split and Equilibrium Assignment Models," Transportation Science, INFORMS, vol. 13(4), pages 292-314, November.
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