Skip to main content
SpringerLink
Log in

Competitive routing of traffic flows by navigation providers

  • Large Scale Systems Control
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

This paper studies a game-theoretic model of traffic flow assignment with multiple customer groups and the BPR delay function on a parallel channel network. We prove the existence of a unique Nash equilibrium in the game of m ≥ 2 traffic navigation providers and derive explicit expressions for equilibrium strategies. And finally, we show that the competition of navigation providers on the network increases the average travel time between origin and destination areas.

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.

Similar content being viewed by others

References

  1. Gasnikov, A.V., Klenov, S.L., Nurminskii, E.A., Holodov, Y.A., and Shamrai, N.B., Vvedenie v matematicheskoe modelirovanie transportnykh potokov (Introduction to Mathematical Modeling of Traffic Flows), Gasnikov, A.V., Ed., Moscow: MFTI, 2010.

  2. Zakharov, V.V. and Krilatov, A.Yu., System Optimum of Traffic Flows in a Megapolis and Strategies of Navigation Providers: The Game-Theoretic Approach, Mat. Teor. Igr Prilozh., 2012, vol. 4, no. 4, pp. 23–44.

    MATH  Google Scholar 

  3. Zorkaltsev, V.I. and Kiseleva, M.A., Nash Equilibrium in Transport Model with Quadratic Costs, Diskr. Anal. Issled. Oper., 2008, vol. 15, no. 3, pp. 31–42.

    MathSciNet  Google Scholar 

  4. Krylatov, A.Yu., Optimal Strategy for the Management of Traffic Flows on a Network of Parallel Channels, Vest. S.-Peterburg. Univ., Ser. 10, Prikl. Mat. Inf. Prots. Upravlen., 2014, no. 2, pp. 121–130.

    Google Scholar 

  5. Shvetsov, V.I., Mathematical Modeling of Traffic Flows, Autom. Remote Control, 2003, vol. 64, no. 11, pp. 1651–1689.

    Article  MathSciNet  MATH  Google Scholar 

  6. Altman, E., Basar, T., Jimenez, T., and Shimkin, N., Competitive Routing in Networks with Polynomial Cost, IEEE Trans. Autom. Control, 2002, vol. 47, no. 1, pp. 92–96.

    Article  MathSciNet  Google Scholar 

  7. Altman, E., Combes, R., Altman, Z., and Sorin, S., Routing Games in the Many Players Regime, in Proc. 5th Int. ICST Conf. on Performance Evaluation Methodologies and Tools, 2011, pp. 525–527.

    Google Scholar 

  8. Altman, E. and Wynter, L., Equilibrium, Games, and Pricing in Transportation and Telecommunication Networks, Networks Spatial Econom., 2004, vol. 4, pp. 7–21.

    Article  MATH  Google Scholar 

  9. Daganzo, C.F., The Cell Transmission Model: A Dynamic Representation of Highway Traffic Consistent with the Hydrodynamic Theory, Transpn. Res. B, 1994, vol. 28, pp. 269–287.

    Article  Google Scholar 

  10. Haurie, A. and Marcotte, P., On the Relationship between Nash–Cournot and Wardrop Equilibria, Networks, 1985, vol. 15, pp. 295–308.

    Article  MathSciNet  MATH  Google Scholar 

  11. Korilis, Y.A., Lazar, A.A., and Orda, A., Architecting Noncooperative Networks, IEEE J. Select. Areas Commun., 1995, vol. 13, no. 7, pp. 1241–1251.

    Article  Google Scholar 

  12. Korilis, Y.A., Lazar, A.A., and Orda, A., Avoiding the Braess Paradox in Non-Cooperative Networks, J. Appl. Prob., 1999, vol. 36, pp. 211–222.

    Article  MathSciNet  MATH  Google Scholar 

  13. Orda, A., Rom, R., and Shimkin, N., Competitive Routing in Multiuser Communication Networks, IEEE/ACM Trans. Network., 1993, vol. 1, no. 5, pp. 510–521.

    Article  Google Scholar 

  14. Sheffi, Y., Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods, Englewood Cliffs: Prentice Hall, 1985.

    Google Scholar 

  15. Traffic Assignment Manual, Washington: US Dept. of Commerce, US Bureau of Public Roads, 1964.

  16. Wardrop, J.G., Some Theoretical Aspects of Road Traffic Research, Proc. Inst. Civ. Eng., 1952, part 2, no. 1, pp. 325–378.

    Google Scholar 

  17. Yang, H. and Huang, H.-J., The Multi-Class, Multi-Criteria Traffic Network Equilibrium and Systems Optimum Problem, Transp. Res. B, 2004, vol. 38, pp. 1–15.

    Article  Google Scholar 

  18. Zakharov, V., Krylatov, A., and Ivanov, D., Equilibrium Traffic Flow Assignment in Case of Two Navigation Providers, in Collaborative Systems for Reindustrialization, Proc. 14th IFIP Conference on Virtual Enterprises PRO-VE 2013, Dresden: Springer, 2013, pp. 156–163.

    Google Scholar 

  19. Zhuge, H., Semantic Linking through Spaces for Cyber-Physical-Socio Intelligence: A Methodology, Artif. Intell., 2011, vol. 175, no. 5, pp. 988–1019.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Saint Petersburg State University, St. Petersburg, Russia

    V. V. Zakharov & A. Yu. Krylatov

  2. Solomenko Institute of Transport Problems, Russian Academy of Sciences, St. Petersburg, Russia

    A. Yu. Krylatov

Authors
  1. V. V. Zakharov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Yu. Krylatov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Zakharov.

Additional information

Original Russian Text © V.V. Zakharov, A.Yu. Krylatov, 2014, published in Upravlenie Bol’shimi Sistemami, 2014, No. 49, pp. 129–147.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zakharov, V.V., Krylatov, A.Y. Competitive routing of traffic flows by navigation providers. Autom Remote Control 77, 179–189 (2016). https://doi.org/10.1134/S0005117916010112

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117916010112

Keywords

Search

Navigation