IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v15y2015i3p583-598.html
   My bibliography  Save this article

A Comparison of Dynamic User Optimal States with Zero, Fixed and Variable Tolerances

Author

Listed:
  • Y. Ge
  • B. Sun
  • H. Zhang
  • W. Szeto
  • Xizhao Zhou

Abstract

The notion of dynamic user equilibrium (DUE) and dynamic user optimum (DUO) were still treated interchangeably in the dynamic traffic assignment (DTA) literature until tolerance-based DUO was recently proposed as alternative definitions of DUO. The latter distinguishes DUO from DUE, and the tolerances can be prescribed a priori (i.e. DUO with fixed tolerance) or endogenously (i.e. DUO with variable tolerance). These tolerances reflect the differences in travel costs between used paths of an origin–destination (OD) pair. Since DUE requires zero difference in travel costs between used paths of an OD pair, it can be regarded as DUO with zero tolerance. This paper first compares the three alternative definitions of DUO and discusses their relationships. Secondly, the existence conditions of these DUO solutions are discussed. A key conclusion is that DUO with variable tolerance always exists even when the other two types of DUO solutions may not. The second conclusion is that, when the tolerances are equal to zero, the solution must be a DUE solution. Furthermore, DUE is a special case of DUO with variable tolerance; since the tolerance in the concept of DUO with variable tolerance is an endogenous variable, if a DUE solution exists, an efficient method for solving for DUO with variable tolerance should directly find such a DUE solution. All these are illustrated by means of three examples. Finally, it is acknowledged that the analysis of DUO with variable tolerance in the same rigor as that of DUE is a challenging problem and worthy of further research. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Y. Ge & B. Sun & H. Zhang & W. Szeto & Xizhao Zhou, 2015. "A Comparison of Dynamic User Optimal States with Zero, Fixed and Variable Tolerances," Networks and Spatial Economics, Springer, vol. 15(3), pages 583-598, September.
    • Handle: RePEc:kap:netspa:v:15:y:2015:i:3:p:583-598
    DOI: 10.1007/s11067-014-9243-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11067-014-9243-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-014-9243-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Malachy Carey & Y. E. Ge, 2005. "Alternative Conditions for a Well-Behaved Travel Time Model," Transportation Science, INFORMS, vol. 39(3), pages 417-428, August.
    2. Bin Ran & David E. Boyce & Larry J. LeBlanc, 1993. "A New Class of Instantaneous Dynamic User-Optimal Traffic Assignment Models," Operations Research, INFORMS, vol. 41(1), pages 192-202, February.
    3. Hani Mahmassani & Robert Herman, 1984. "Dynamic User Equilibrium Departure Time and Route Choice on Idealized Traffic Arterials," Transportation Science, INFORMS, vol. 18(4), pages 362-384, November.
    4. Smith, M. J., 1984. "Two alternative definitions of traffic equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 18(1), pages 63-65, February.
    5. Wie, Byung-Wook & Friesz, Terry L. & Tobin, Roger L., 1990. "Dynamic user optimal traffic assignment on congested multidestination networks," Transportation Research Part B: Methodological, Elsevier, vol. 24(6), pages 431-442, December.
    6. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
    7. Hani S. Mahmassani & Gang-Len Chang, 1987. "On Boundedly Rational User Equilibrium in Transportation Systems," Transportation Science, INFORMS, vol. 21(2), pages 89-99, May.
    8. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    9. Yu Nie & H. Zhang, 2010. "Solving the Dynamic User Optimal Assignment Problem Considering Queue Spillback," Networks and Spatial Economics, Springer, vol. 10(1), pages 49-71, March.
    10. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
    11. Friesz, Terry L. & Kim, Taeil & Kwon, Changhyun & Rigdon, Matthew A., 2011. "Approximate network loading and dual-time-scale dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 176-207, January.
    12. Heydecker, B. G., 1986. "On the definition of traffic equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 20(6), pages 435-440, December.
    13. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    14. Herbert A. Simon, 1991. "Bounded Rationality and Organizational Learning," Organization Science, INFORMS, vol. 2(1), pages 125-134, February.
    15. Guo, Xiaolei & Liu, Henry X., 2011. "Bounded rationality and irreversible network change," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1606-1618.
    16. F. H. Knight, 1924. "Some Fallacies in the Interpretation of Social Cost," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 38(4), pages 582-606.
    17. Feng Xiao & Zhen Qian & H. Zhang, 2011. "The Morning Commute Problem with Coarse Toll and Nonidentical Commuters," Networks and Spatial Economics, Springer, vol. 11(2), pages 343-369, June.
    18. Daoli Zhu & Patrice Marcotte, 2000. "On the Existence of Solutions to the Dynamic User Equilibrium Problem," Transportation Science, INFORMS, vol. 34(4), pages 402-414, November.
    19. Papageorgiou, Markos, 1990. "Dynamic modeling, assignment, and route guidance in traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 24(6), pages 471-495, December.
    20. Xiao, Feng & Shen, Wei & Michael Zhang, H., 2012. "The morning commute under flat toll and tactical waiting," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1346-1359.
    21. Chen-Hsiu Laih, 2004. "Effects of the optimal step toll scheme on equilibrium commuter behaviour," Applied Economics, Taylor & Francis Journals, vol. 36(1), pages 59-81.
    22. Szeto, W. Y. & Lo, Hong K., 2004. "A cell-based simultaneous route and departure time choice model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 593-612, August.
    Full references (including those not matched with items on IDEAS)

    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. Han, Ke & Szeto, W.Y. & Friesz, Terry L., 2015. "Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 16-49.
    2. Tong, C. O. & Wong, S. C., 2000. "A predictive dynamic traffic assignment model in congested capacity-constrained road networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 625-644, November.
    3. Ke Han & Gabriel Eve & Terry L. Friesz, 2019. "Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation," Networks and Spatial Economics, Springer, vol. 19(3), pages 869-902, September.
    4. Han, Ke & Friesz, Terry L. & Szeto, W.Y. & Liu, Hongcheng, 2015. "Elastic demand dynamic network user equilibrium: Formulation, existence and computation," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 183-209.
    5. Song, Wenjing & Han, Ke & Wang, Yiou & Friesz, Terry L. & del Castillo, Enrique, 2018. "Statistical metamodeling of dynamic network loading," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 740-756.
    6. Friesz, Terry L. & Kim, Taeil & Kwon, Changhyun & Rigdon, Matthew A., 2011. "Approximate network loading and dual-time-scale dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 176-207, January.
    7. Qixiu Cheng & Zhiyuan Liu & Feifei Liu & Ruo Jia, 2017. "Urban dynamic congestion pricing: an overview and emerging research needs," International Journal of Urban Sciences, Taylor & Francis Journals, vol. 21(0), pages 3-18, August.
    8. Babak Javani & Abbas Babazadeh, 2020. "Path-Based Dynamic User Equilibrium Model with Applications to Strategic Transportation Planning," Networks and Spatial Economics, Springer, vol. 20(2), pages 329-366, June.
    9. Yu, Hao & Ma, Rui & Zhang, H. Michael, 2018. "Optimal traffic signal control under dynamic user equilibrium and link constraints in a general network," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 302-325.
    10. Long, Jiancheng & Szeto, W.Y. & Gao, Ziyou & Huang, Hai-Jun & Shi, Qin, 2016. "The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 179-206.
    11. Ke Han & Terry L. Friesz, 2017. "Continuity of the Effective Delay Operator for Networks Based on the Link Delay Model," Networks and Spatial Economics, Springer, vol. 17(4), pages 1095-1110, December.
    12. Friesz, Terry L. & Han, Ke & Neto, Pedro A. & Meimand, Amir & Yao, Tao, 2013. "Dynamic user equilibrium based on a hydrodynamic model," Transportation Research Part B: Methodological, Elsevier, vol. 47(C), pages 102-126.
    13. Lu, Gongyuan & Nie, Yu(Marco) & Liu, Xiaobo & Li, Denghui, 2019. "Trajectory-based traffic management inside an autonomous vehicle zone," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 76-98.
    14. Friesz, Terry L. & Han, Ke, 2019. "The mathematical foundations of dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 309-328.
    15. Ran, Bin & Boyce, David E., 1995. "Ideal Dynamic User-Optimal Route Choice: A Link-Based Variational Inequality Formulation," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3t4686x6, Institute of Transportation Studies, UC Berkeley.
    16. Duong Viet Thong & Aviv Gibali & Mathias Staudigl & Phan Tu Vuong, 2021. "Computing Dynamic User Equilibrium on Large-Scale Networks Without Knowing Global Parameters," Networks and Spatial Economics, Springer, vol. 21(3), pages 735-768, September.
    17. Chen, Hongyu & Nie, Yu (Marco) & Yin, Yafeng, 2015. "Optimal multi-step toll design under general user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 775-793.
    18. Ran, Bin & Hall, Randolph & Boyce, David E., 1995. "A Link-Based Variational Inequality Model for Dynamic Departure Time/Route Choice," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt84t190b3, Institute of Transportation Studies, UC Berkeley.
    19. van den Berg, Vincent A.C., 2014. "Coarse tolling with heterogeneous preferences," Transportation Research Part B: Methodological, Elsevier, vol. 64(C), pages 1-23.
    20. Bellei, Giuseppe & Gentile, Guido & Papola, Natale, 2005. "A within-day dynamic traffic assignment model for urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 39(1), pages 1-29, January.

    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:kap:netspa:v:15:y:2015:i:3:p:583-598. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.