On Packet Scheduling with Adversarial Jamming and Speedup

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 simple 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 maintains 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. Furthermore, we show a lower bound of φ+1 ≈ 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. 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]. Finally, we obtain a lower bound of 2 on the speedup of any 1-competitive deterministic algorithm using only two divisible packet sizes, which is tight.