IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v40y2006i8p633-650.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191-2615(05)00104-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ye, Jiao & Jiang, Yu & Chen, Jun & Liu, Zhiyuan & Guo, Renzhong, 2021. "Joint optimisation of transfer location and capacity for a capacitated multimodal transport network with elastic demand: a bi-level programming model and paradoxes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).
    2. Karakaya, Emrah, 2016. "Finite Element Method for forecasting the diffusion of photovoltaic systems: Why and how?," Applied Energy, Elsevier, vol. 163(C), pages 464-475.
    3. Yao, Jia & Chen, Anthony & Ryu, Seungkyu & Shi, Feng, 2014. "A general unconstrained optimization formulation for the combined distribution and assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 137-160.
    4. Xu, Meng & Chen, Anthony & Gao, Ziyou, 2008. "An improved origin-based algorithm for solving the combined distribution and assignment problem," European Journal of Operational Research, Elsevier, vol. 188(2), pages 354-369, July.
    5. Du, Bo & Wang, David Z.W., 2014. "Continuum modeling of park-and-ride services considering travel time reliability and heterogeneous commuters – A linear complementarity system approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 58-81.
    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.
    8. Long, Jiancheng & Szeto, W.Y. & Du, Jie & Wong, R.C.P., 2017. "A dynamic taxi traffic assignment model: A two-level continuum transportation system approach," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 222-254.
    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.
    15. Faping Wang & Rui Chen & Lixin Miao & Peng Yang & Bin Ye, 2019. "Location Optimization of Electric Vehicle Mobile Charging Stations Considering Multi-Period Stochastic User Equilibrium," Sustainability, MDPI, vol. 11(20), pages 1-19, October.
    16. Zhi-Yang Lin & S. C. Wong & Peng Zhang & Keechoo Choi, 2018. "A Predictive Continuum Dynamic User-Optimal Model for the Simultaneous Departure Time and Route Choice Problem in a Polycentric City," Service Science, INFORMS, vol. 52(6), pages 1496-1508, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Xu, Meng & Chen, Anthony & Gao, Ziyou, 2008. "An improved origin-based algorithm for solving the combined distribution and assignment problem," European Journal of Operational Research, Elsevier, vol. 188(2), pages 354-369, July.
    5. Cantarella, Giulio Erberto & Cartenì, Armando & de Luca, Stefano, 2015. "Stochastic equilibrium assignment with variable demand: Theoretical and implementation issues," European Journal of Operational Research, Elsevier, vol. 241(2), pages 330-347.
    6. David Boyce, 2007. "Forecasting Travel on Congested Urban Transportation Networks: Review and Prospects for Network Equilibrium Models," Networks and Spatial Economics, Springer, vol. 7(2), pages 99-128, June.
    7. 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.
    8. García, Ricardo & Marín, Angel, 2005. "Network equilibrium with combined modes: models and solution algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 39(3), pages 223-254, March.
    9. Karakaya, Emrah, 2016. "Finite Element Method for forecasting the diffusion of photovoltaic systems: Why and how?," Applied Energy, Elsevier, vol. 163(C), pages 464-475.
    10. 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.
    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. 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.
    13. Lam, William H. K. & Tam, M. L., 1997. "Why standard modelling and evaluation procedures are inadequate for assessing traffic congestion measures," Transport Policy, Elsevier, vol. 4(4), pages 217-223, October.
    14. Vo, Khoa D. & Lam, William H.K. & Chen, Anthony & Shao, Hu, 2020. "A household optimum utility approach for modeling joint activity-travel choices in congested road networks," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 93-125.
    15. Bar-Gera, Hillel & Boyce, David, 2006. "Solving a non-convex combined travel forecasting model by the method of successive averages with constant step sizes," Transportation Research Part B: Methodological, Elsevier, vol. 40(5), pages 351-367, June.
    16. 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.
    17. Li, Zhi-Chun & Wang, Ya-Dong, 2018. "Analysis of multimodal two-dimensional urban system equilibrium for cordon toll pricing and bus service design," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 244-265.
    18. 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.
    19. Li, Zhi-Chun & Chen, Ya-Juan & Wang, Ya-Dong & Lam, William H.K. & Wong, S.C., 2013. "Optimal density of radial major roads in a two-dimensional monocentric city with endogenous residential distribution and housing prices," Regional Science and Urban Economics, Elsevier, vol. 43(6), pages 927-937.
    20. Yang, Chao & Chen, Anthony, 2009. "Sensitivity analysis of the combined travel demand model with applications," European Journal of Operational Research, Elsevier, vol. 198(3), pages 909-921, November.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:40:y:2006:i:8:p:633-650. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.