A 4/3-competitive randomized algorithm for online scheduling of packets with agreeable deadlines

TL;DR

This paper simplifies a deterministic online packet scheduling algorithm with agreeable deadlines and introduces randomness, achieving a 4/3-competitive ratio against oblivious adversaries, narrowing the gap with the lower bound.

Contribution

The authors simplify an existing algorithm and incorporate randomness to improve the competitive ratio for online packet scheduling with agreeable deadlines.

Findings

Simplified the Li et al. algorithm without losing competitiveness.

Achieved a 4/3-competitive ratio with the randomized algorithm.

Identified a gap between current upper bound and lower bound for randomized algorithms.

Abstract

In 2005 Li et al. gave a phi-competitive deterministic online algorithm for scheduling of packets with agreeable deadlines with a very interesting analysis. This is known to be optimal due to a lower bound by Hajek. We claim that the algorithm by Li et al. can be slightly simplified, while retaining its competitive ratio. Then we introduce randomness to the modified algorithm and argue that the competitive ratio against oblivious adversary is at most 4/3. Note that this still leaves a gap between the best known lower bound of 5/4 by Chin et al. for randomised algorithms against oblivious adversary.