An Optimal Lower Bound for Buffer Management in Multi-Queue Switches

TL;DR

This paper establishes a tight lower bound of approximately 1.582 on the competitive ratio for online buffer management in multi-queue switches, improving previous bounds and analyzing the performance of existing algorithms.

Contribution

It provides the first tight lower bound for the problem, matching the Random Schedule algorithm's performance and correcting previous misconceptions about Random Permutation.

Findings

Lower bound of e/(e-1) for competitive ratio

Improved lower bound from 1.4659 to 1.582

Identification of flaws in the analysis of Random Permutation

Abstract

In the online packet buffering problem (also known as the unweighted FIFO variant of buffer management), we focus on a single network packet switching device with several input ports and one output port. This device forwards unit-size, unit-value packets from input ports to the output port. Buffers attached to input ports may accumulate incoming packets for later transmission; if they cannot accommodate all incoming packets, their excess is lost. A packet buffering algorithm has to choose from which buffers to transmit packets in order to minimize the number of lost packets and thus maximize the throughput. We present a tight lower bound of e/(e-1) ~ 1.582 on the competitive ratio of the throughput maximization, which holds even for fractional or randomized algorithms. This improves the previously best known lower bound of 1.4659 and matches the performance of the algorithm Random Schedule. Our result contradicts the claimed performance of the algorithm Random Permutation; we point out a flaw in its original analysis.