Skip to main content
Springer Nature Link
Log in

User Equilibrium and System Optimality Conditions for Flow Distributions on Congested Networks

  • Conference paper
  • First Online:
Engineering Applications of Neural Networks (EANN 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1826))

Abstract

Motivated by flow allocation in communication and transportation networks we examine user equilibrium and system optimal flows on networks of parallel links. User equilibrium is achieved when the journey times on all the used routes are equal and less than any other unused route. On the other hand the system optimal flow minimizes the average journey times for all used routes. In this paper we study the connection between user equilibrium and system optimums and investigate networks that have identical user equilibrium and system optimal flows. We identify a correspondence between the system optimum of a network and the user equilibrium of the associated Pigovian network and use it to show uniqueness of the system optimum. Using a characterization of Wardrop optimal flows for differentiable convex networks, we show that they are preserved via continuous, strictly increasing and convex functions, uniform increase or decrease of the latency functions and network addition and multiplication.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Beckmann, M.J., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. RAND Corporation (1955)

    Google Scholar 

  2. Dafermos, S., Sparrow, F.: The traffic assignment problem for a general network. J. Res. National Bureau of Standards-B. Math. Sci. 73(2), 91–118 (1969)

    Google Scholar 

  3. Kalampakas, A., Aifantis, E.: Random walk on graphs: an application to the double diffusivity model. Mech. Res. Commun. 43, 101–104 (2012)

    Article  Google Scholar 

  4. Kalampakas, A.: The syntactic complexity of eulerian graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 4728 LNCS, pp. 208–217 (2007)

    Google Scholar 

  5. Kalampakas, A.: Graph automata: The algebraic properties of abelian relational graphoids. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 7020 LNCS, pp. 168–182 (2011)

    Google Scholar 

  6. Kalampakas, A.: Graph automata and graph colorability. Europ. J. Pure Appl. Mathe. 16(1), 112–120 (2023)

    Article  MathSciNet  Google Scholar 

  7. Kalampakas, A., Spartalis, S.: Path hypergroupoids: Commutativity and graph connectivity. Europ. J. Combinat. 44(PB), 257–264 (2015)

    Google Scholar 

  8. Kalampakas, A., Spartalis, S., Iliadis, L., Pimenidis, E.: Fuzzy graphs: algebraic structure and syntactic recognition. Artif. Intell. Rev. 42(3), 479–490 (2014)

    Article  Google Scholar 

  9. Kalampakas, A., Spartalis, S., Tsigkas, A.: The path hyperoperation. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica 22(1), 141–153 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kelly, F.P., Maulloo, A.K., Tan, D.K.H.: Rate control for communication networks: shadow prices, proportional fairness and stability. J. Oper. Res. Soci. 49(3), 237–252 (1998)

    Article  MATH  Google Scholar 

  11. Low, S., Lapsley, D.: Optimization flow control. i. basic algorithm and convergence. IEEE/ACM Trans. Network.7(6), 861–874 (1999)

    Google Scholar 

  12. Pigou, A.C.: The Economics of Welfare. Macmillan, London (1920)

    Google Scholar 

  13. Saburov, M.: On replicator equations with nonlinear payoff functions defined by the ricker models. Adv. Pure Appl. Math. 12, 39–156 (2021)

    Article  Google Scholar 

  14. Saburov, M.: On discrete-time replicator equations with nonlinear payoff functions. Dyn. Games Appl. 12, 643–661 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sanghavi, S., Hajek, B.: Optimal allocation of a divisible good to strategic buyers. In: 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). vol. 3, pp. 2748–2753 Vol. 3 (2004)

    Google Scholar 

  16. Wardrop, J.G.: Some theoretical aspects of road traffic research. In: Proceedings of the Institute of Civil Engineers, Part II, 1, 325–378 3, pp. 325–362 (1952)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Engineering and Technology, American University of the Middle East, Egaila, 54200, Kuwait

    Antonios Kalampakas, Armen Bagdasaryan & Mansoor Saburov

  2. Department of Production and Management Engineering, Laboratory of Computational Mathematics, School of Engineering, Democritus University of Thrace, V. Sofias 12, Prokat, Building A1, 67132, Xanthi, Greece

    Stefanos Spartalis

  3. School of Science and Technology, Studies in Physics, Hellenic Open University, 18 Aristoteles Bystreet, 26335, Patra, Greece

    Stefanos Spartalis

Authors
  1. Antonios Kalampakas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Armen Bagdasaryan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mansoor Saburov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Stefanos Spartalis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonios Kalampakas .

Editor information

Editors and Affiliations

  1. Democritus University of Thrace, Xanthi, Greece

    Lazaros Iliadis

  2. University of Piraeus, Piraeus, Greece

    Ilias Maglogiannis

  3. University of Leon, León, Spain

    Serafin Alonso

  4. Teesside University, Middlesbrough, UK

    Chrisina Jayne

  5. University of the West of England, Bristol, UK

    Elias Pimenidis

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kalampakas, A., Bagdasaryan, A., Saburov, M., Spartalis, S. (2023). User Equilibrium and System Optimality Conditions for Flow Distributions on Congested Networks. In: Iliadis, L., Maglogiannis, I., Alonso, S., Jayne, C., Pimenidis, E. (eds) Engineering Applications of Neural Networks. EANN 2023. Communications in Computer and Information Science, vol 1826. Springer, Cham. https://doi.org/10.1007/978-3-031-34204-2_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-34204-2_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-34203-5

  • Online ISBN: 978-3-031-34204-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics