Heterogenous Networks Can Be Unstable at Arbitrarily Low Injection Rates

  • Dimitrios Koukopoulos
  • Stavros D. Nikolopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3998)


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 for such common settings of heterogeneous distributed systems concerns their ability to preserve or restore an acceptable level of performance during link failures. In this work, we address this question for the specific case of stability properties of greedy, contention-resolution protocols operating over a packet-switched communication network that suffers from link slowdowns. We focus on the Adversarial Queueing Theory framework, where an adversary controls the rates of packet injections and determines packet paths. In addition, the power of the adversary is enhanced to include the manipulation of link slowdowns. Within this framework, we show that the composition of LIS (Longest-in-System) with any of SIS (Shortest-in-System), NTS (Nearest-to-Source) and FTG (Furthest-to-Go) protocols is unstable at rates ρ > 0 when the network size and the link slowdown take large values. These results represent the current record for instability bounds on injection rate for compositions of greedy protocols over dynamic adversarial models, and also suggest that the potential for instability incurred by the composition of two greedy protocols may be worse than that of some single protocol.


Injection Rate Heterogenous Network Link Failure Network Queue Instability Bound 
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.


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  1. 1.
    Àlvarez, C., Blesa, M.J., Díaz, J., Fernández, A., Serna, M.: Adversarial Models for Priority-Based Networks. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 142–151. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Alvarez, C., Blesa, M., Serna, M.: A Characterization of Universal Stability in the Adversarial Queuing model. SIAM Journal on Computing 34, 41–66 (2004)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Alvarez, C., Blesa, M., Serna, M.: The Impact of Failure Management on the Stability of Communication Networks. In: Proc. of the 10th Int’l Conference on Parallel and Distributed Systems, pp. 153–160 (2004)Google Scholar
  4. 4.
    Andrews, M., Awerbuch, B., Fernández, A., Kleinberg, J., Leighton, T., Liu, Z.: Universal Stability Results for Greedy Contention-Resolution Protocols. Journal of the ACM 48, 39–69 (2001)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Barlow, R., Proschan, F.: Statistical Analysis of Reliability and LifeTesting Models. Holt, Rinehart and Winston, New York (1975)Google Scholar
  6. 6.
    Blesa, M., Calzada, D., Fernández, A., López, L., Martínez, A., Santos, A., Serna, M.: Adversarial Queueing Model for Continuous Network Dynamics. In: Jedrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol. 3618, pp. 144–155. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Borodin, A., Kleinberg, J., Raghavan, P., Sudan, M., Williamson, D.: Adversarial Queueing Theory. Journal of the ACM 48, 13–38 (2001)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Borodin, A., Ostrovsky, R., Rabani, Y.: Stability Preserving Transformations: Packet Routing Networks with Edge Capacities and Speeds. In: Proc. of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 601–610 (2001)Google Scholar
  9. 9.
    Clark, D.: The Design Philosophy of the DARPA Internet Protocols. ACM Computer Communication Reviews 18, 106–114 (1988)CrossRefGoogle Scholar
  10. 10.
    Diaz, J., Koukopoulos, D., Nikoletseas, S., Serna, M., Spirakis, P., Thilikos, D.: Stability and Non-Stability of the FIFO Protocol. In: Proc. of the 13th Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 48–52 (2001)Google Scholar
  11. 11.
    Floyd, S., Paxson, V.: Difficulties in Simulating the Internet. IEEE/ACM Transactions on Networking 9, 392–403 (2001)CrossRefGoogle Scholar
  12. 12.
    Gary, J.: Why do computers stop and what can be done about it? In: Symposium on Reliability in Distributed Software and Database Systems (1986)Google Scholar
  13. 13.
    Herlihy, M.P., Wing, J.: Linearizability: A Correctness Condition for Concurrent Objects. Proc. of the ACM Transactions on Programming Languages and Systems 12(3), 463–492 (1990)CrossRefGoogle Scholar
  14. 14.
    Koukopoulos, D.: The Impact of Dynamic Link Slowdowns on Network Stability. In: Proc. of the 8th Int’l Symposium on Parallel Architectures, Algorithms and Networks, pp. 340–345 (2005)Google Scholar
  15. 15.
    Koukopoulos, D., Mavronicolas, M., Nikoletseas, S., Spirakis, P.: On the Stability of Compositions of Universally Stable, Greedy, Contention-Resolution Protocols. In: Malkhi, D. (ed.) DISC 2002. LNCS, vol. 2508, pp. 88–102. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Koukopoulos, D., Mavronicolas, M., Nikoletseas, S., Spirakis, P.: The Impact of Network Structure on the Stability of Greedy Protocols. Theory of Computing Systems 38, 425–460 (2005)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Koukopoulos, D., Nikoletseas, S., Spirakis, P.: Stability Issues in Heterogeneous and FIFO Networks under the Adversarial Queueing Model. In: Monien, B., Prasanna, V.K., Vajapeyam, S. (eds.) HiPC 2001. LNCS, vol. 2228, pp. 3–14. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  18. 18.
    Koukopoulos, D., Mavronicolas, M., Spirakis, P.: Instability of Networks with Quasi-Static Link Capacities. In: Proc. of the 10th Int’l Colloquium on Structural Information and Communication Complexity, Carleton Scientific, pp. 179–194 (2003)Google Scholar
  19. 19.
    Lotker, Z., Patt-Shamir, B., Rosén, A.: New Stability Results for Adversarial Queuing. SIAM Journal on Computing 33, 286–303 (2004)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Lynch, N.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)MATHGoogle Scholar
  21. 21.
    Tsaparas, P.: Stability in Adversarial Queueing Theory, M.Sc. Thesis, Computer Science Department, University of Toronto (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Dimitrios Koukopoulos
    • 1
  • Stavros D. Nikolopoulos
    • 2
  1. 1.Department of Cultural Heritage Management & New TechnologiesUniversity of IoanninaAgrinioGreece
  2. 2.Department of Computer ScienceUniversity of IoanninaIoanninaGreece

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