Skip to main content

User Equilibrium in a Transportation Space-Time Network

  • Chapter
  • First Online:
Optimisation in Synchromodal Logistics

Part of the book series: Lecture Notes in Operations Research ((LNOR))

Abstract

This chapter focuses on synchromodal planning problems in which information is shared between all agents in the system and they choose their routes based on an individual optimisation objective. We show the effect of the information availability by developing three different methods to determine the optimal paths, to motivate logistic players to cooperate in a synchromodal system.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bar-Gera, H. (1999). Origin-based algorithms for transportation network modeling. Ph.D. thesis, Chicago: University of Illinois at Chicago.

    Google Scholar 

  2. Bar-Gera, H., Boyce, D., & Nie, Y.M. (2012). User-equilibrium route flows and the condition of proportionality. Transportation Research Part B: Methodological, 46(3), 440–462.

    Article  Google Scholar 

  3. Corman, F., Viti, F., & Negenborn, R. R. (2017). Equilibrium models in multimodal container transport systems. Flexible Services and Manufacturing Journal, 29(1), 125–153.

    Article  Google Scholar 

  4. Didi-Biha, M., Marcotte, P., & Savard, G. (2006). Path-based formulations of a bilevel toll setting problem. In Optimization with Multivalued Mappings (pp. 29–50). Springer

    Google Scholar 

  5. van Essen, M., Thomas, T., van Berkum, E., & Chorus, C. (2016). From user equilibrium to system optimum: a literature review on the role of travel information, bounded rationality and non-selfish behaviour at the network and individual levels. Transport Reviews, 36(4), 527–548.

    Article  Google Scholar 

  6. Florian, M., & Hearn, D. (2003). Network equilibrium and pricing. In Handbook of Transportation Science (pp. 373–411). Springer

    Google Scholar 

  7. Han, D., & Yang, H. (2008). The multi-class, multi-criterion traffic equilibrium and the efficiency of congestion pricing. Transportation Research Part E: Logistics and Transportation Review, 44(5), 753–773.

    Article  Google Scholar 

  8. Hearn, D., & Ramana, M. (1998). Solving congestion toll pricing models. In P. Marcotte, & S. Nguyen (Eds.), Equilibrium and Advanced Transportation Modelling. Centre for Research on Transportation.

    Google Scholar 

  9. Jiang, L., & Mahmassani, H. (2013). Toll pricing: Computational tests for capturing heterogeneity of user preferences. Transportation Research Record: Journal of the Transportation Research Board, 2343(1), 105–115.

    Article  Google Scholar 

  10. Levy, N., Klein, I., & Ben-Elia, E. (2016). Emergence of cooperation and a fair system optimum in road networks: A game-theoretic and agent-based modelling approach. Research in Transportation Economic, 68, 46–55.

    Article  Google Scholar 

  11. Liu, C. L., & Liu, F. (2012). Dynamical consensus seeking of second-order multi-agent systems based on delayed state compensation. Systems & Control Letters, 61(12), 1235–1241.

    Article  Google Scholar 

  12. Miyagi, T., & Peque, G. C. (2012). Informed-user algorithms that converge to Nash equilibrium in traffic games. Procedia—Social and Behavioral Sciences, 54, 438–449. https://doi.org/10.1016/j.sbspro.2012.09.762. Proceedings of EWGT2012—15th Meeting of the EURO Working Group on Transportation, September 2012, Paris.

  13. Peeta, S., & Mahmassani, H. S. (1995). System optimal and user equilibrium time-dependent traffic assignment in congested networks. Annals of Operations Research, 60(1), 81–113.

    Article  Google Scholar 

  14. Ren, W., & Beard, R. W. (2005). Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 50(5), 655–661.

    Article  Google Scholar 

  15. Roughgarden, T. (2006). Selfish routing and the price of anarchy. OPTIMA-2007.

    Google Scholar 

  16. Wagner, N. (2012). The dynamic user equilibrium on a transport network: Mathematical properties and economic applications. Ph.D. thesis, Université Paris-Est.

    Google Scholar 

  17. Wang, C., & Tang, Y. (2017). The discussion of system optimism and user equilibrium in traffic assignment with the perspective of game theory. Transportation Research Procedia, 25, 2974–2983.

    Article  Google Scholar 

  18. Xu, W., Miao, L., & Lin, W. H. (2012). Stochastic user equilibrium assignment in schedule-based transit networks with capacity constraints. In Discrete Dynamics in Nature and Society

    Google Scholar 

  19. Yang, H., & Huang, H. J. (2005). Fundamentals of user-equilibrium problems. In Mathematical and Economic Theory of Road Pricing (pp. 13–46). Amsterdam: Elsevier.

    Chapter  Google Scholar 

  20. Yang, H., & Huang, H. J. (2005). Social and spatial equities and revenue redistribution. In Mathematical and Economic Theory of Road Pricing (pp. 203–238). Amsterdam: Elsevier.

    Chapter  Google Scholar 

  21. Yang, H., & Zhang, X. (2008). Existence of anonymous link tolls for system optimum on networks with mixed equilibrium behaviors. Transportation Research Part B: Methodological, 42(2), 99–112 .

    Article  Google Scholar 

  22. Roughgarden, T., & Tardos, E. (2002). How bad is selfish routing? Journal of the ACM (JACM), 49(2), 236–259.

    Article  Google Scholar 

  23. Swamy, C. (2007). The effectiveness of stackelberg strategies and tolls for network congestion games. In Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms (pp. 1133–1142). Society for Industrial and Applied Mathematics.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 Netherlands Organisation for Applied Scientific Research

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bruijns, L.A.M. (2023). User Equilibrium in a Transportation Space-Time Network. In: Phillipson, F. (eds) Optimisation in Synchromodal Logistics. Lecture Notes in Operations Research. Springer, Cham. https://doi.org/10.1007/978-3-031-15655-7_11

Download citation

Publish with us

Policies and ethics