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Adversarial Models for Priority-Based Networks

  • C. Àlvarez
  • M. Blesa
  • J. Díaz
  • A. Fernández
  • M. Serna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)

Abstract

We propose several variations of the adversarial queueing model to cope with packets that can have different priorities, the priority and variable priority models, and link failures, the failure and reliable models. We address stability issues in the proposed adversarial models. We show that the set of universally stable networks in the adversarial model remains the same in the four introduced models. From the point of view of queueing policies we show that several queueing policies that are universally stable in the adversarial model remain so in the priority, failure and reliable models. However, we show that lis, a universally stable queueing policy in the adversarial model, is not universally stable in any of the other models, and that no greedy queueing policy is universally stable in the variable priority model. Finally we analyze the problem of deciding stability of a given network under a fixed protocol. We provide a characterization of the networks that are stable under fifo and lis in the failure model. This characterization allows us to show that deciding network stability under fifo and lis in the proposed models can be solved in polynomial time.

Keywords

Polynomial Time Injection Rate Dynamic Network Reliable Model Failure Model 
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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References

  1. 1.
    Àlvarez, C., Blesa, M., Díaz, J., Fernández, A., Serna, M.: Adversarial models for priority-based networks. Technical Report LSI-03-25-R, Software department, Universitat Politècnica de Catalunya (2003) Google Scholar
  2. 2.
    Àlvarez, C., Blesa, M., Díaz, J., Fernández, A., Serna, M.: The complexity of deciding stability under FFS in the adversarial model. Technical Report LSI-03-16-R, Software department, Universitat Politècnica de Catalunya (2003) Google Scholar
  3. 3.
    Àlvarez, C., Blesa, M., Serna, M.: A characterization of universal stability in the adversarial queueing model. Technical Report LSI-03-27-R, Software department, Universitat Politècnica de Catalunya (2003) Google Scholar
  4. 4.
    Àlvarez, C., Blesa, M., Serna, M.: Universal stability of undirected graphs in the adversarial queueing model. In: 14th ACM Symposium on Parallel Algorithms and Architectures (SPAA 2002), Winnipeg, Canada, pp. 183–197. ACM Press, New York (August 2002)CrossRefGoogle Scholar
  5. 5.
    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(1), 39–69 (2001)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Anshelevich, E., Kempe, D., Kleinberg, J.: Stability of load balancing algorithms in dynamic adversarial systems. In: 34th. ACM Symposium on Theory of Computing (STOC 2002), pp. 399–406 (2002)Google Scholar
  7. 7.
    Awerbuch, B., Berenbrink, P., Brinkmann, A., Scheideler, C.: Simple routing strategies for adversarial systems. In: 42th. IEEE Symposium on Foundations of Computer Science (FOCS 2001), pp. 158–167 (2001)Google Scholar
  8. 8.
    Bhattacharjee, R., Goel, A.: Instability of FIFO at arbitrarily low rates in the adversarial queueing model. Technical Report 02-776, Department of Computer Science, University of Southern California, Los Angeles, USA (2002) Google Scholar
  9. 9.
    Borodin, A., Ostrovsky, R., Rabani, Y.: Stability Preserving Transformations: Packet Routing Networks with Edge Capacities and Speeds. In: ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), pp. 601–610 (2001)Google Scholar
  10. 10.
    Borodin, A., Kleinberg, J., Raghavan, P., Sudan, M., Williamson, D.: Adversarial queueing theory. Journal of the ACM 48(1), 13–38 (2001)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Charny, A., Le Boudec, J.-Y.: Delay Bounds in a Network With Aggregate Scheduling. In: Proc. First International Workshop on Quality of future Internet Services, Berlin, Germany (2000)Google Scholar
  12. 12.
    Diaz, J., Koukopoulos, D., Nikoletseas, S., Serna, M., Spirakis, P., Thilikós, D.: Stability and non-Stability of the FIFO Protocol. In: 13th annual ACM Symposium on Parallel Algorithms and Architectures (SPAA 2001), pp. 48–52 (2001)Google Scholar
  13. 13.
    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
  14. 14.
    Koukopoulos, D., Mavronicolas, M., Spirakis, P.: FIFO is unstable at arbitrarily low rates. ECCC, TR-03-16 (2003) Google Scholar
  15. 15.
    Lotker, Z., Patt-Shamir, B., Rosén, A.: New stability results for adversarial queuing. In: 14th ACM Symposium on Parallel Algorithms and Architectures (SPAA 2002), Winnipeg, Canada, pp. 175–182 (2002)Google Scholar
  16. 16.
    Rosén, A.: A note on models for non-probabilistic analysis of packet switching networks. Information Processing Letters 84, 237–240 (2002)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • C. Àlvarez
    • 1
  • M. Blesa
    • 1
  • J. Díaz
    • 1
  • A. Fernández
    • 2
  • M. Serna
    • 1
  1. 1.Dept. de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelona
  2. 2.Dept. Ciencias Experimentales e IngenieríaUniversidad Rey Juan CarlosMadrid

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