Buffer Overflow Management with Class Segregation

TL;DR

This paper studies buffer management for network switches with QoS, analyzing a greedy algorithm's competitiveness and establishing bounds for optimal online algorithms in class-segregated queues.

Contribution

It introduces a new model for buffer management with class segregation and provides competitive ratio bounds for a natural greedy algorithm.

Findings

GREEDY is (1+r)-competitive for general values, with r depending on value ratios.

Lower bounds are established for the competitiveness of any deterministic online algorithm.

GREEDY is optimal for two-value cases, with a specific competitive ratio.

Abstract

We consider a new model for buffer management of network switches with Quality of Service (QoS) requirements. A stream of packets, each attributed with a value representing its Class of Service (CoS), arrives over time at a network switch and demands a further transmission. The switch is equipped with multiple queues of limited capacities, where each queue stores packets of one value only. The objective is to maximize the total value of the transmitted packets (i.e., the weighted throughput). We analyze a natural greedy algorithm, GREEDY, which sends in each time step a packet with the greatest value. For general packet values $(v_1 < \cdots < v_m)$, we show that GREEDY is $(1+r)$-competitive, where $r = \max_{1\le i \le m-1} \{v_i/v_{i+1}\}$. Furthermore, we show a lower bound of $2 - v_m / \sum_{i=1}^m v_i$ on the competitiveness of any deterministic online algorithm. In the special case of two packet values (1 and $\alpha > 1$), GREEDY is shown to be optimal with a competitive ratio of $(\alpha + 2)/(\alpha + 1)$.