Skip to main content
Springer Nature Link
Log in

Existence and Uniqueness of Equilibria for Flows over Time

  • Conference paper
Automata, Languages and Programming (ICALP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6756))

Included in the following conference series:

  • 1542 Accesses

Abstract

Network flows that vary over time arise naturally when modeling rapidly evolving systems such as the Internet. In this paper, we continue the study of equilibria for flows over time in the single-source single-sink deterministic queuing model proposed by Koch and Skutella. We give a constructive proof for the existence and uniqueness of equilibria for the case of a piecewise constant inflow rate, through a detailed analysis of the static flows obtained as derivatives of a dynamic equilibrium.

Supported in part by Instituto Milenio Sistemas Complejos de Ingeniería, and FONDECYT grants 1090050 and 1100046.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Anderson, E.J., Philpott, A.B.: Optimisation of flows in networks over time. In: Kelly, F.P. (ed.) Probability, Statistics and Optimisation, pp. 369–382. Wiley, New York (1994)

    Google Scholar 

  2. Bhaskar, U., Fleischer, L., Anshelevich, E.: A stackelberg strategy for routing flow over time. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 192–201 (2011)

    Google Scholar 

  3. Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, New York (2010)

    Book  Google Scholar 

  4. Facchinei, F., Pang, J.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. I. Springer, New York (2003)

    MATH  Google Scholar 

  5. Fleischer, L., Tardos, E.: Efficient continuous-time dynamic network flow algorithms. Operations Research 23(3-5), 71–80 (1998)

    MATH  MathSciNet  Google Scholar 

  6. Ford, L.R., Fulkerson, D.R.: Constructing maximal dynamic flows from static flows. Operations Research 6, 419–433 (1958)

    Article  MathSciNet  Google Scholar 

  7. Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (1962)

    MATH  Google Scholar 

  8. Gale, D.: Transient flows in networks. Michigan Mathematical Journal 6, 59–63 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  9. Koch, R., Skutella, M.: Nash equilibria and the price of anarchy for flows over time. Theory of Computing Systems (to appear)

    Google Scholar 

  10. Macko, M., Larson, K., Steskal, Ľ.: Braess’s Paradox for Flows over Time. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) Algorithmic Game Theory. LNCS, vol. 6386, pp. 262–275. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  11. Ran, B., Boyce, D.: Modeling Dynamic Transportation Networks. Springer, Berlin (1996)

    Book  MATH  Google Scholar 

  12. Skutella, M.: An introduction to network flows over time. In: Cook, W., Lovasz, L., Vygen, J. (eds.) Research Trends in Combinatorial Optimization, pp. 451–482. Springer, Berlin (2009)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Universidad de Chile, Santiago, Chile

    Roberto Cominetti, José R. Correa & Omar Larré

Authors
  1. Roberto Cominetti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. José R. Correa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Omar Larré
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. ICE-TCS, School of Computer Science, Reykjavik University, Menntavegur 1, IS 101, Reykjavik, Iceland

    Luca Aceto

  2. Fakultät für Informatik, Universität Wien, Universitätsstraße10/9, 1090, Wien, Österreich, Austria

    Monika Henzinger

  3. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Jiří Sgall

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cominetti, R., Correa, J.R., Larré, O. (2011). Existence and Uniqueness of Equilibria for Flows over Time. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22012-8_44

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22012-8_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22011-1

  • Online ISBN: 978-3-642-22012-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics