On the Stability of Compositions of Universally Stable, Greedy Contention-Resolution Protocols

  • D. Koukopoulos
  • M. Mavronicolas
  • S. Nikoletseas
  • P. Spirakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2508)


A distinguishing feature of today’s large-scale platforms for distributed computation and communication, such as the Internet, is their heterogeneity, predominantly manifested by the fact that a wide variety of communication protocols are simultaneously running over different distributed hosts. A fundamental question that naturally poses itself concerns the preservation (or loss) of important correctness and performance properties of the individual protocols when they are composed in a large network. In this work, we specifically address stability properties of greedy, contention-resolution protocols operating over a packet-switched communication network.

We focus on a basic adversarial model for packet arrival and path determination for which the time-averaged arrival rate of packets requiring a single edge is no more than 1. Stability requires that the number of packets in the system remains bounded, as the system runs for an arbitrarily long period of time. It is known that several commonly used contention-resolution protocols, such as LIS (Longest-in-System), SIS (Shortest-in-System), NTS (Nearest-to-Source), and FTG (Furthest-to-Go) are universally stable in this setting - that is, they are stable over all networks. We investigate the preservation of universal stability under compositions for these four greedy, contention-resolution protocols. We discover:
  • — The composition of any two protocols among SIS, NTS and FTG is universally stable.

  • — The composition of LIS with any of SIS, NTS and FTG is not universally stable: we provide interesting combinatorial constructions of networks over which the composition is unstable when the adversary’s injection rate is at least 0.519.

  • — Through an involved combinatorial construction, we significantly improve the current state-of-the-art record for the adversary’s injection rate that implies instability for FIFO protocol to 0.749. Since 0.519 is significantly below 0.749, this last result suggests that the potential for instability incurred by the composition of two universally stable protocols may be worse than that of some single protocol that is not universally stable.


Induction Hypothesis Injection Rate Induction Step Packet Arrival Instability Threshold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Andrews, B. Awerbuch, A. Fernandez, J. Kleinberg, T. Leighton, and Z. Liu, “Universal Stability Results for Greedy Contention-Resolution Protocols,” Journal of the ACM, Vol. 48, No. 1, pp. 39–69, January 2001.CrossRefMathSciNetGoogle Scholar
  2. 2.
    M. Andrews, A. Férnandez, A. Goel and L. Zhang, “Source Routing and Scheduling in Packet Networks,” Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, pp. 168–177, October 2002.Google Scholar
  3. 3.
    A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan and D. Williamson, “Adversarial Queueing Theory,” Journal of the ACM, Vol. 48, No. 1, pp. 13–38, January 2001.CrossRefMathSciNetGoogle Scholar
  4. 4.
    H. Chen and D.D. Yao, Fundamentals of Queueing Networks, Springer, 2000.Google Scholar
  5. 5.
    J. Diaz, D. Koukopoulos, S. Nikoletseas, M. Serna, P. Spirakis and D. Thilikos, “Stability and Non-Stability of the FIFO Protocol,” Proceedings of the 13th Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 48–52, July 2001.Google Scholar
  6. 6.
    A. Férnandez, E. Jiménez and V. Cholvi, “On the Interconnection of Causal Memory Systems,” Proceedings of the 19th Annual ACM Symposium on Principles of Distributed Computing, pp. 163–170, July 2000.Google Scholar
  7. 7.
    S. Floyd and V. Paxson, “Difficulties in Simulating the Internet,” IEEE/ACM Transactions on Networking, Vol. 9, No. 4, pp. 392–403, August 2001.CrossRefGoogle Scholar
  8. 8.
    A. Goel, “Stability of Networks and Protocols in the Adversarial Queueing Model for Packet Routing,” Networks, Vol. 37, No. 4, pp. 219–224, 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    M. P. Herlihy and J. Wing, “Linearizability: A Correctness Condition for Concurrent Objects,” ACM Transactions on Programming Languages and Systems, Vol. 12, No. 3, pp. 463–492, 1990.CrossRefGoogle Scholar
  10. 10.
    N. Lynch, Distributed Algorithms, Morgan Kaufmann, 1996.Google Scholar
  11. 11.
    J. Mitchell, Email Communication to I. Lee, April 2002.Google Scholar
  12. 12.
    P. Tsaparas, Stability in Adversarial Queueing Theory, M.Sc. Thesis. Department of Computer Science, University of Toronto, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • D. Koukopoulos
    • 1
  • M. Mavronicolas
    • 2
  • S. Nikoletseas
    • 1
  • P. Spirakis
    • 1
  1. 1.Department of Computer Engineering & InformaticsUniversity of Patras and Computer Technology Institute (CTI)PatrasGreece
  2. 2.Department of Computer ScienceUniversity of CyprusNicosiaCyprus

Personalised recommendations