Skip to main content
SpringerLink
Log in

Alpha-reliable combined mean traffic equilibrium model with stochastic travel times

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

Based on the reliability budget and percentile travel time (PTT) concept, a new travel time index named combined mean travel time (CMTT) under stochastic traffic network was proposed. CMTT here was defined as the convex combination of the conditional expectations of PTT-below and PTT-excess travel times. The former was designed as a risk-optimistic travel time index, and the latter was a risk-pessimistic one. Hence, CMTT was able to describe various routing risk-attitudes. The central idea of CMTT was comprehensively illustrated and the difference among the existing travel time indices was analyzed. The Wardropian combined mean traffic equilibrium (CMTE) model was formulated as a variational inequality and solved via an alternating direction algorithm nesting extra-gradient projection process. Some mathematical properties of CMTT and CMTE model were rigorously proved. Finally, a numerical example was performed to characterize the CMTE network. It is founded that that risk-pessimism is of more benefit to a modest (or low) congestion and risk network, however, it changes to be risk-optimism for a high congestion and risk network.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. FRANK H. Shortest paths in probabilistic graphs [J]. Operations Research, 1969, 17(4): 583–599.

    Article  MATH  MathSciNet  Google Scholar 

  2. FAN Y, KALABA R, MOORE J. Arriving on time [J]. Journal of Optimization Theory and Application, 2005, 127(3): 497–513.

    Article  MATH  MathSciNet  Google Scholar 

  3. LEVY H. Stochastic dominance: Investment decision making under uncertainty [M]. New York: Springer, 2006: 147–152.

    Google Scholar 

  4. NIE Y, WU X. Shortest path problem considering on-time arrival probability [J]. Transportation Research Part B, 2009, 43(6): 597–613.

    Article  MathSciNet  Google Scholar 

  5. NIE Y, WU X. Reliable a priori shortest path problem with limited spatial and temporal dependencies [C]// Proceedings of the 18th International Symposium on Transportation and Traffic Theory, Hong Kong. Springer, 2009: 169–195.

    Google Scholar 

  6. NIE Y. Multi-class percentile user equilibrium with flow-dependent stochasticity [J]. Transportation Research Part B, 2011, 45(10): 1641–1659.

    Article  Google Scholar 

  7. HALL R W. The fastest path through a network with random time-dependent travel time [J]. Transportation Science, 1986, 20(3): 182–186.

    Article  Google Scholar 

  8. WU X, NIE Y. Modelling heterogeneous risk-taking behaviour in route choice: A stochastic dominance approach [J]. Transportation Research A, 2011, 45(9): 896–915.

    Google Scholar 

  9. LO H K, TUNG Y K. Network with degradable links: Capacity analysis and design [J]. Transportation Research Part B, 2003, 37(4): 345–363.

    Article  Google Scholar 

  10. LO H K, LUO X W, SIU B W Y. Degradable transport network: Travel time budget of travellers with heterogeneous risk aversion [J]. Transportation Research Part B, 2006, 40(9): 792–806.

    Article  Google Scholar 

  11. ARTZNER P, DELBAEN F, EBER J M, HEATH D. Coherent measures of risk [J]. Mathematical Finance, 1999, 9(3): 203–228.

    Article  MATH  MathSciNet  Google Scholar 

  12. CHEN A, JI Z W. Path finding under uncertainty [J]. Journal of Advanced Transportation, 2005, 39(1): 19–37.

    Article  MathSciNet  Google Scholar 

  13. SHAO H, LAM W H K, TAM M L. A reliability-based stochastic traffic assignment model for network with multiple user classes under uncertain in demand [J]. Network and Spatial Economics, 2006, 6(3/4): 313–332.

    MathSciNet  Google Scholar 

  14. SIU B W Y, LO H K. Doubly uncertain transport network: Degradable link capacity and perception variation in traffic conditions [J]. Transportation Research Record, 2006, 1964: 59–69.

    Article  Google Scholar 

  15. SHAO H, LAM W H K, TAM M L, YUAN X M. Modelling rain effects on risk-taking behaviours of multi-user classes in road networks with uncertainty [J]. Journal of Advanced Transportation, 2008, 42(3): 265–290.

    Article  Google Scholar 

  16. LAM W H K, SHAO H, SUMALEE A. Modelling impacts of adverse weather conditions on a road network with uncertainties in demand and supply [J]. Transportation Research Part B, 2008, 42(10): 890–910.

    Article  Google Scholar 

  17. CHEN A, ZHOU Z. The alpha-reliable mean-excess traffic equilibrium model with stochastic travel times [J]. Transportation Research Part B, 2010, 44(4): 493–513.

    Article  Google Scholar 

  18. ROCKAFELLAR R T, URYASEV S. Optimization of conditional value-at-risk [J]. Journal of Risk, 2000, 2(3): 21–41.

    Google Scholar 

  19. FOSGERAU M, KARLSTROM A. The value of reliability [J]. Transportation Research Part B, 2010, 44(1): 38–49.

    Article  Google Scholar 

  20. FOSGERAU M, ENGELSON L. The value of travel time variance [J]. Transportation Research Part B, 2011, 45(1): 1–8.

    Article  Google Scholar 

  21. ORDONEZ F, STIER-MOSES N E. Wardrop equilibria with risk-averse users [J]. Transportation Science, 2010, 44(1): 63–86.

    Article  Google Scholar 

  22. NG M W, SZETO W Y, WALLER S T. Distribution-free travel time reliability assessment with probability inequalities [J]. Transportation Research Part B, 2011, 45(6): 852–866.

    Article  Google Scholar 

  23. GERVAIS S, HEATON J B, ODEAN T. Overconfidence, investment policy, and executive stock options [R]. Rodney L. White Center for Financial Research Working Paper No. 15-02, 2002.

    Google Scholar 

  24. BILINGSLEY P. Probability and measure [M]. New York: John Wiley and Sons, Inc., 1995: 359–363.

    Google Scholar 

  25. FACCHINEI F, PANG J S. Finite-dimensional variational inequalities and complementarity problems [M]. New York: Springer, 2003: 41–46.

    Google Scholar 

  26. NAGURNEY A. Network economics: A variational inequality approach [M]. Dordrecht: Kluwer Academic Publishers, 1993: 14–15.

    Book  Google Scholar 

  27. HAN D. A modified alternating direction method for variational inequation problems [J]. Applied Mathematics and Optimization, 2002, 45(1): 63–74.

    Article  MATH  MathSciNet  Google Scholar 

  28. KORPELEVICH G M. The extra-gradient method for finding saddle points and other problems [J]. Matecon, 1976, 12: 747–756.

    MATH  Google Scholar 

  29. HAN Ji-ye, XIU Nai-hua, QI Hou-duo. Nonlinear complementarity theory and algorithms [M]. Shanghai: Shanghai Scientific & Technical Publishers, 2006: 132–141. (in Chinese)

    Google Scholar 

  30. ZHOU Z, CHEN A. Comparative analysis of three user equilibrium models under stochastic demand [J]. Journal of Advanced Transportation, 2008, 42(3): 239–263.

    Article  Google Scholar 

  31. LIU Tian-liang, HUANG Hai-jun, TIAN Li-jun. Microscopic simulation of multi-lane traffic under dynamic tolling and information feedback [J]. Journal of Central South University of Technology, 2009, 16(5): 865–870.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory for Urban Transportation Complex Systems Theory and Technology of Ministry of Education, Beijing Jiaotong University, Beijing, 100044, China

    Wen-yi Zhang  (张文义), Wei Guan  (关伟), Li-ying Song  (宋丽英) & Hui-jun Sun  (孙会君)

Authors
  1. Wen-yi Zhang  (张文义)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Guan  (关伟)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Li-ying Song  (宋丽英)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hui-jun Sun  (孙会君)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Guan  (关伟).

Additional information

Foundation item: Project(2012CB725403-5) supported by National Basic Research Program of China; Project(71131001-2) supported by National Natural Science Foundation of China; Projects(2012JBZ005) supported by Fundamental Research Funds for the Central Universities, China; Project(201170) supported by the Foundation for National Excellent Doctoral Dissertation of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Wy., Guan, W., Song, Ly. et al. Alpha-reliable combined mean traffic equilibrium model with stochastic travel times. J. Cent. South Univ. 20, 3770–3778 (2013). https://doi.org/10.1007/s11771-013-1906-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-013-1906-z

Key words

Search

Navigation