Randomised Buffer Management with Bounded Delay against Adaptive Adversary

TL;DR

This paper presents a new analysis of the RMix algorithm for buffer management with bounded delay, demonstrating its competitiveness against adaptive adversaries, extending previous proofs to more general online scheduling problems.

Contribution

The paper provides a novel proof of the RMix algorithm's competitiveness that holds against adaptive adversaries, broadening its theoretical guarantees.

Findings

The analysis confirms RMix's competitiveness in adaptive adversary models.

The proof extends to a more general online scheduling problem.

The competitiveness ratio remains e/(e-1) under new conditions.

Abstract

We give a new analysis of the RMix algorithm by Chin et al. for the Buffer Management with Bounded Delay problem (or online scheduling of unit jobs to maximise weighted throughput). Unlike the original proof of e/(e-1)-competitiveness, the new one holds even in adaptive-online adversary model. In fact, the proof works also for a slightly more general problem studied by Bie{\'n}kowski et al.