Skip to main content
SpringerLink
Log in

Heavy Traffic Approximation of Equilibria in Resource Sharing Games

  • Conference paper
Internet and Network Economics (WINE 2011)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7090))

Included in the following conference series:

Abstract

We consider a model of priced resource sharing that combines both queueing behavior and strategic behavior. We study a priority service model where a single server allocates its capacity to agents in proportion to their payment to the system, and users from different classes act to minimize the sum of their cost for processing delay and payment. As the exact processing time of this system is hard to compute, we introduce the notion of heavy traffic equilibrium as an approximation of the Nash equilibrium, derived by considering the asymptotic regime where the system load approaches capacity. We discuss efficiency and revenue, and in particular provide a bound for the price of anarchy of the heavy traffic equilibrium.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allon, G., Gurvich, I.: Pricing and dimensioning competing large-scale service providers. Manufacturing & Service Operations Management 12, 449–469 (2010)

    Article  Google Scholar 

  2. Altman, E., Avrachenkov, K., Ayesta, U.: A survey on discriminatory processor sharing. Queueing Systems 53(1-2), 53–63 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Billingsley, P.: Weak Convergence of Measures: Applications in Probability. Society for Industrial Mathematics, Philadelphia (1987)

    MATH  Google Scholar 

  4. Chen, Y., Maglaras, C., Vulcano, G.: Design of an aggregated marketplace under congestion effects: Asymptotic analysis and equilibrium characterization (2010) Working Paper

    Google Scholar 

  5. Cox, D.R., Smith, W.L.: Queues. Methuen and Wiley, London and New York (1961)

    Google Scholar 

  6. Fayolle, G., Mitrani, I., Iasnogorodski, R.: Sharing a processor among many job classes. Journal of the ACM 27(3), 519–532 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hassin, R., Haviv, M.: To queue or not to queue: Equilibrium behavior in queueing systems. Kluwer Academic Publishers (2003)

    Google Scholar 

  8. Haviv, M., van der Wal, J.: Equilibrium strategies for processor sharing and queues with relative priorities. Probability in the Engineering and Informational Sciences 11(4), 403–412 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kang, W., Kelly, F., Lee, N., Williams, R.: State space collapse and diffusion approximation for a network operation under a fair bandwidth sharing policy. The Annals of Applied Probability 19(5), 1719–1780 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kelly, F.P., Maulloo, A., Tan, D.: Rate control in communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research Society 49(3), 237–252 (1998)

    Article  MATH  Google Scholar 

  11. Kingman, J.F.C.: On queues in heavy traffic. Journal of the Royal Statistical Society. Series B (Methodological) 24(2), 383–392 (1962)

    MathSciNet  MATH  Google Scholar 

  12. Kleinrock, L.: Time-shared systems: A theoretical treatment. Journal of ACM 14(2), 242–261 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kleinrock, L.: Queueing Systems: Theory, vol. 1. Wiley–Interscience, New York (1975)

    MATH  Google Scholar 

  14. Massoulié, L., Roberts, J.: Bandwidth sharing and admission control for elastic traffic. Telecommunication Systems 15(1-2), 185–201 (2000)

    Article  MATH  Google Scholar 

  15. Mo, J., Walrand, J.: Fair end-to-end window-based congestion control. IEEE/ACM Trans. Netw. 8, 556–567 (2000)

    Article  Google Scholar 

  16. Naor, P.: The regulation of queue size by levying tolls. Econometrica 37(1), 15–24 (1969)

    Article  MATH  Google Scholar 

  17. Rege, K., Sengupta, B.: Queue-length distribution for the discriminatory processor-sharing queue. Operations Research 44(4), 653–657 (1996)

    Article  MATH  Google Scholar 

  18. Reiman, M.I.: Open queueing networks in heavy traffic. Mathematics of Operations Research 9(3), 441–458 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  19. Verloop, I.M., Ayesta, U., Nunez-Queija, R.: Heavy-traffic analysis of a multiple-phase network with discriminatory processor sharing. Operations Research 59(3), 648–660 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wu, Y., Bui, L., Johari, R.: Heavy traffic approximations of equilibria in resource sharing games. Technical Report, arXiv:1109.6166 (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MS&E, Stanford University, USA

    Yu Wu, Loc Bui & Ramesh Johari

Authors
  1. Yu Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Loc Bui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ramesh Johari
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. GECAD, Instituto Superior de Engenharia do Porto, Portugal

    Ning Chen

  2. School of Physical and Mathematical Sciences, SPMS-MAS-03-01, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore

    Edith Elkind

  3. Department of Informatics, University of Athens, Greece

    Elias Koutsoupias

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wu, Y., Bui, L., Johari, R. (2011). Heavy Traffic Approximation of Equilibria in Resource Sharing Games. In: Chen, N., Elkind, E., Koutsoupias, E. (eds) Internet and Network Economics. WINE 2011. Lecture Notes in Computer Science, vol 7090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25510-6_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25510-6_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25509-0

  • Online ISBN: 978-3-642-25510-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation