WINE 2011: Internet and Network Economics pp 351-362 | Cite as

Heavy Traffic Approximation of Equilibria in Resource Sharing Games

  • Yu Wu
  • Loc Bui
  • Ramesh Johari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)

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.

Keywords

resource sharing discriminatory processor sharing equilibrium heavy traffic approximation 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allon, G., Gurvich, I.: Pricing and dimensioning competing large-scale service providers. Manufacturing & Service Operations Management 12, 449–469 (2010)CrossRefGoogle Scholar
  2. 2.
    Altman, E., Avrachenkov, K., Ayesta, U.: A survey on discriminatory processor sharing. Queueing Systems 53(1-2), 53–63 (2006)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Billingsley, P.: Weak Convergence of Measures: Applications in Probability. Society for Industrial Mathematics, Philadelphia (1987)MATHGoogle Scholar
  4. 4.
    Chen, Y., Maglaras, C., Vulcano, G.: Design of an aggregated marketplace under congestion effects: Asymptotic analysis and equilibrium characterization (2010) Working PaperGoogle Scholar
  5. 5.
    Cox, D.R., Smith, W.L.: Queues. Methuen and Wiley, London and New York (1961)Google Scholar
  6. 6.
    Fayolle, G., Mitrani, I., Iasnogorodski, R.: Sharing a processor among many job classes. Journal of the ACM 27(3), 519–532 (1980)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Hassin, R., Haviv, M.: To queue or not to queue: Equilibrium behavior in queueing systems. Kluwer Academic Publishers (2003)Google Scholar
  8. 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)MathSciNetCrossRefMATHGoogle Scholar
  9. 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)MathSciNetCrossRefMATHGoogle Scholar
  10. 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)CrossRefMATHGoogle Scholar
  11. 11.
    Kingman, J.F.C.: On queues in heavy traffic. Journal of the Royal Statistical Society. Series B (Methodological) 24(2), 383–392 (1962)MathSciNetMATHGoogle Scholar
  12. 12.
    Kleinrock, L.: Time-shared systems: A theoretical treatment. Journal of ACM 14(2), 242–261 (1967)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Kleinrock, L.: Queueing Systems: Theory, vol. 1. Wiley–Interscience, New York (1975)MATHGoogle Scholar
  14. 14.
    Massoulié, L., Roberts, J.: Bandwidth sharing and admission control for elastic traffic. Telecommunication Systems 15(1-2), 185–201 (2000)CrossRefMATHGoogle Scholar
  15. 15.
    Mo, J., Walrand, J.: Fair end-to-end window-based congestion control. IEEE/ACM Trans. Netw. 8, 556–567 (2000)CrossRefGoogle Scholar
  16. 16.
    Naor, P.: The regulation of queue size by levying tolls. Econometrica 37(1), 15–24 (1969)CrossRefMATHGoogle Scholar
  17. 17.
    Rege, K., Sengupta, B.: Queue-length distribution for the discriminatory processor-sharing queue. Operations Research 44(4), 653–657 (1996)CrossRefMATHGoogle Scholar
  18. 18.
    Reiman, M.I.: Open queueing networks in heavy traffic. Mathematics of Operations Research 9(3), 441–458 (1984)MathSciNetCrossRefMATHGoogle Scholar
  19. 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)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Wu, Y., Bui, L., Johari, R.: Heavy traffic approximations of equilibria in resource sharing games. Technical Report, arXiv:1109.6166 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yu Wu
    • 1
  • Loc Bui
    • 1
  • Ramesh Johari
    • 1
  1. 1.MS&EStanford UniversityUSA

Personalised recommendations