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].
M. Böhm, J. Sgall and P. Veselý—Supported by the project 17-09142S of GA ČR and by the project 634217 of GAUK.
L. Jeż—Supported by Polish National Science Center grant 2016/21/D/ST6/02402.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
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_1
Fernández Anta, A., Georgiou, C., Kowalski, D.R., Zavou, E.: Online parallel scheduling of non-uniform tasks. Theor. Comput. Sci. 590, 129–146 (2015)
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)
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 2017
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)
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_17
Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. J. ACM 47(4), 617–643 (2000)
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)
Lam, T.W., Ngan, T.-W., To, T.-T.: Performance guarantee for EDF under overload. J. Algorithms 52, 193–206 (2004)
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)
Phillips, C.A., Stein, C., Torng, E., Wein, J.: Optimal time-critical scheduling via resource augmentation. Algorithmica 32, 163–200 (2002)
Schewior, K.: Deadline scheduling and convex-body chasing. Ph.D dissertation, TU Berlin (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Böhm, M., Jeż, Ł., Sgall, J., Veselý, P. (2018). On Packet Scheduling with Adversarial Jamming and Speedup. In: Solis-Oba, R., Fleischer, R. (eds) Approximation and Online Algorithms. WAOA 2017. Lecture Notes in Computer Science(), vol 10787. Springer, Cham. https://doi.org/10.1007/978-3-319-89441-6_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-89441-6_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-89440-9
Online ISBN: 978-3-319-89441-6
eBook Packages: Computer ScienceComputer Science (R0)