Advertisement

On Packet Scheduling with Adversarial Jamming and Speedup

  • Martin Böhm
  • Łukasz Jeż
  • Jiří Sgall
  • Pavel VeselýEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10787)

Abstract

In Packet Scheduling with Adversarial Jamming packets of arbitrary sizes arrive over time to be transmitted over a channel in which instantaneous jamming errors occur at times chosen by the adversary and not known to the algorithm. The transmission taking place at the time of jamming is corrupt, and the algorithm learns this fact immediately. An online algorithm maximizes the total size of packets it successfully transmits and the goal is to develop an algorithm with the lowest possible asymptotic competitive ratio, where the additive constant may depend on packet sizes.

Our main contribution is a universal algorithm that works for any speedup and packet sizes and, unlike previous algorithms for the problem, it does not need to know these properties in advance. We show that this algorithm guarantees 1-competitiveness with speedup 4, making it the first known algorithm to maintain 1-competitiveness with a moderate speedup in the general setting of arbitrary packet sizes. We also prove a lower bound of \(\phi +1\approx 2.618\) on the speedup of any 1-competitive deterministic algorithm, showing that our algorithm is close to the optimum. Additionally, we formulate a general framework for analyzing our algorithm locally and use it to show upper bounds on its competitive ratio for speedups in [1, 4) and for several special cases, recovering some previously known results, each of which had a dedicated proof. In particular, our algorithm is 3-competitive without speedup, matching the algorithm and the lower bound of Jurdzinski et al. [7]. We use this framework also for the case of divisible packet sizes in which the size of a packet divides the size of any larger packet, to show that a slight modification of our algorithm is 1-competitive with speedup 2 and it achieves the optimal competitive ratio of 2 without speedup, again matching the algorithm and the lower bound of [7].

References

  1. 1.
    Fernández Anta, A., Georgiou, C., Kowalski, D.R., Widmer, J., Zavou, E.: Measuring the impact of adversarial errors on packet scheduling strategies. J. Sched. 19(2), 135–152 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Fernández Anta, A., Georgiou, C., Kowalski, D.R., Zavou, E.: Competitive analysis of task scheduling algorithms on a fault-prone machine and the impact of resource augmentation. In: Pop, F., Potop-Butucaru, M. (eds.) ARMS-CC 2015. LNCS, vol. 9438, pp. 1–16. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-28448-4_1CrossRefGoogle Scholar
  3. 3.
    Fernández Anta, A., Georgiou, C., Kowalski, D.R., Zavou, E.: Online parallel scheduling of non-uniform tasks. Theor. Comput. Sci. 590, 129–146 (2015)CrossRefzbMATHGoogle Scholar
  4. 4.
    Chrobak, M., Epstein, L., Noga, J., Sgall, J., van Stee, R., Tichý, T., Vakhania, N.: Preemptive scheduling in overloaded systems. J. Comput. Syst. Sci. 67, 183–197 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Garncarek, P., Jurdziński, T., Loryś, K.: Fault-tolerant online packet scheduling on parallel channels. In: 2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 347–356, May 2017Google Scholar
  6. 6.
    Georgiou, C., Kowalski, D.R.: On the competitiveness of scheduling dynamically injected tasks on processes prone to crashes and restarts. J. Parallel Distrib. Comput. 84, 94–107 (2015)CrossRefGoogle Scholar
  7. 7.
    Jurdzinski, T., Kowalski, D.R., Lorys, K.: Online packet scheduling under adversarial jamming. In: Bampis, E., Svensson, O. (eds.) WAOA 2014. LNCS, vol. 8952, pp. 193–206. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-18263-6_17Google Scholar
  8. 8.
    Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. J. ACM 47(4), 617–643 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Koo, C.-Y., Lam, T.W., Ngan, T.-W., Sadakane, K., To, K.-K.: On-line scheduling with tight deadlines. Theor. Comput. Sci. 295, 251–261 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Lam, T.W., Ngan, T.-W., To, T.-T.: Performance guarantee for EDF under overload. J. Algorithms 52, 193–206 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lam, T.W., To, K.-K.: Trade-offs between speed and processor in hard-deadline scheduling. In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 623–632. ACM/SIAM (1999)Google Scholar
  12. 12.
    Phillips, C.A., Stein, C., Torng, E., Wein, J.: Optimal time-critical scheduling via resource augmentation. Algorithmica 32, 163–200 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Schewior, K.: Deadline scheduling and convex-body chasing. Ph.D dissertation, TU Berlin (2016)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Martin Böhm
    • 1
  • Łukasz Jeż
    • 2
  • Jiří Sgall
    • 1
  • Pavel Veselý
    • 1
    Email author
  1. 1.Computer Science Institute of Charles UniversityPragueCzech Republic
  2. 2.Institute of Computer ScienceUniversity of WrocławWrocławPoland

Personalised recommendations