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.
Work partially supported by the FET Programme of the EU under contract number IST-2001-33116 (FLAGS), and by the Spanish CICYT project TIC-2001-4917-E. The second author was also supported by the Catalan government with the pre-doctoral grant 2001FI-00659.
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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)
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)
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)
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)
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)
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)
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)
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)
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)
Borodin, A., Kleinberg, J., Raghavan, P., Sudan, M., Williamson, D.: Adversarial queueing theory. Journal of the ACM 48(1), 13–38 (2001)
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)
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)
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)
Koukopoulos, D., Mavronicolas, M., Spirakis, P.: FIFO is unstable at arbitrarily low rates. ECCC, TR-03-16 (2003)
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)
Rosén, A.: A note on models for non-probabilistic analysis of packet switching networks. Information Processing Letters 84, 237–240 (2002)
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Àlvarez, C., Blesa, M., Díaz, J., Fernández, A., Serna, M. (2003). Adversarial Models for Priority-Based Networks. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_8
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DOI: https://doi.org/10.1007/978-3-540-45138-9_8
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