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Combined distribution and assignment model for a continuum traffic equilibrium problem with multiple user classes

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  • Ho, H.W.
  • Wong, S.C.
  • Loo, Becky P.Y.

Abstract

Consider a city with several facilities competing for multi-class users that are distributed continuously over space. Within the city region, the road network is relatively dense and is considered as a continuum. A user equilibrium condition results when users freely make their choice of facilities and their optimal routes within this continuum based on the criterion of minimizing the total facility and travel cost. A logit-type demand distribution function is specified to model the probabilistic choice behavior of destinations for the multi-class users. Furthermore, facility externality is introduced to capture the effect of congestion and economies of scale, as the usage of the facility varies. A mathematical program is formulated for the above complex problem, and a promising solution algorithm is developed. Finally, a numerical example is given to show the feasibility of the mathematical program and the effectiveness of the solution algorithm.

Suggested Citation

  • Ho, H.W. & Wong, S.C. & Loo, Becky P.Y., 2006. "Combined distribution and assignment model for a continuum traffic equilibrium problem with multiple user classes," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 633-650, September.
    • Handle: RePEc:eee:transb:v:40:y:2006:i:8:p:633-650
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    1. Yang, Hai & Yagar, Sam & Iida, Yasunori, 1994. "Traffic assignment in a congested discrete/ continuous transportation system," Transportation Research Part B: Methodological, Elsevier, vol. 28(2), pages 161-174, April.
    2. Bar-Gera, Hillel & Boyce, David, 2003. "Origin-based algorithms for combined travel forecasting models," Transportation Research Part B: Methodological, Elsevier, vol. 37(5), pages 405-422, June.
    3. 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.
    4. Wong, S. C., 1994. "An alternative formulation of D'Este's trip assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 28(3), pages 187-196, June.
    5. Michalopoulos, Panos G. & Beskos, Dimitrios E. & Lin, Jaw-Kuan, 1984. "Analysis of interrupted traffic flow by finite difference methods," Transportation Research Part B: Methodological, Elsevier, vol. 18(4-5), pages 409-421.
    6. Stella C. Dafermos, 1972. "The Traffic Assignment Problem for Multiclass-User Transportation Networks," Transportation Science, INFORMS, vol. 6(1), pages 73-87, February.
    7. Lam, William H. K. & Huang, Hai-Jun, 1992. "A combined trip distribution and assignment model for multiple user classes," Transportation Research Part B: Methodological, Elsevier, vol. 26(4), pages 275-287, August.
    8. Wong, S. C., 1998. "Multi-commodity traffic assignment by continuum approximation of network flow with variable demand," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 567-581, November.
    9. Buckley, D. J., 1979. "Traffic assignment in a two-dimensional continuous representation of a traffic network with flow-dependent speeds," Transportation Research Part B: Methodological, Elsevier, vol. 13(2), pages 167-179, June.
    10. S. C. Wong & S. H. Sun, 2001. "A combined distribution and assignment model for continuous facility location problem," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 35(2), pages 267-281.
    11. D'Este, Glen, 1987. "Trip assignment to radial major roads," Transportation Research Part B: Methodological, Elsevier, vol. 21(6), pages 433-442, December.
    12. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
    13. D E Boyce, 1984. "Urban Transportation Network-Equilibrium and Design Models: Recent Achievements and Future Prospects," Environment and Planning A, , vol. 16(11), pages 1445-1474, November.
    14. Ho, H.W. & Wong, S.C. & Yang, Hai & Loo, Becky P.Y., 2005. "Cordon-based congestion pricing in a continuum traffic equilibrium system," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 813-834.
    15. T Puu, 1977. "A Proposed Definition of Traffic Flow in Continuous Transportation Models," Environment and Planning A, , vol. 9(5), pages 559-567, May.
    16. Tenny N. Lam & G. F. Newell, 1967. "Flow Dependent Traffic Assignment on a Circular City," Transportation Science, INFORMS, vol. 1(4), pages 318-361, November.
    17. Dafermos, Stella C., 1980. "Continuum modelling of transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 295-301, September.
    18. Lam, William H. K. & Huang, Hai-Jun, 1992. "Calibration of the combined trip distribution and assignment model for multiple user classes," Transportation Research Part B: Methodological, Elsevier, vol. 26(4), pages 289-305, August.
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    6. Liu, Tian-Liang & Huang, Hai-Jun & Yang, Hai & Zhang, Xiaoning, 2009. "Continuum modeling of park-and-ride services in a linear monocentric city with deterministic mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 692-707, July.
    7. Huang, Ling & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Lam, William H.K., 2009. "Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 127-141, January.
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    9. Jiang, Yanqun & Wong, S.C. & Ho, H.W. & Zhang, Peng & Liu, Ruxun & Sumalee, Agachai, 2011. "A dynamic traffic assignment model for a continuum transportation system," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 343-363, February.
    10. Canca, David & Zarzo, Alejandro & Algaba, Encarnación & Barrena, Eva, 2013. "Macroscopic attraction-based simulation of pedestrian mobility: A dynamic individual route-choice approach," European Journal of Operational Research, Elsevier, vol. 231(2), pages 428-442.
    11. Yan-Qun Jiang & S.C. Wong & Peng Zhang & Keechoo Choi, 2017. "Dynamic Continuum Model with Elastic Demand for a Polycentric Urban City," Transportation Science, INFORMS, vol. 51(3), pages 931-945, August.
    12. Jing Gao & Sen Li, 2023. "Regulating For-Hire Autonomous Vehicles for An Equitable Multimodal Transportation Network," Papers 2301.05798, arXiv.org, revised Oct 2023.
    13. Du, Jie & Wong, S.C. & Shu, Chi-Wang & Xiong, Tao & Zhang, Mengping & Choi, Keechoo, 2013. "Revisiting Jiang’s dynamic continuum model for urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 96-119.
    14. Karakaya, Emrah, 2014. "Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems," INDEK Working Paper Series 2014/6, Royal Institute of Technology, Department of Industrial Economics and Management.
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