# On Packet Scheduling with Adversarial Jamming and Speedup

## TL;DR

This paper introduces a universal online packet scheduling algorithm that achieves optimal competitive ratios under adversarial jamming, with a focus on arbitrary packet sizes and unknown system parameters.

## Contribution

It presents the first universal algorithm that guarantees 1-competitiveness with moderate speedup without prior knowledge of packet sizes or speedup, and establishes near-optimal bounds.

## Key findings

- Achieves 1-competitiveness with speedup 4.
- Proves a lower bound of approximately 2.618 on speedup for 1-competitiveness.
- Provides a framework for analyzing competitive ratios across different speedups.

## 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 both the (worst-case) performance of the algorithm by Jurdzinski et al. and the lower bound by Anta et al.