Controlling congestion on complex networks: fairness, efficiency and network structure

TL;DR

This paper analyzes how different congestion control algorithms and network structures influence throughput, fairness, and bottleneck locations, revealing complex interactions especially in scale-free networks and the importance of path flow distributions.

Contribution

It provides a comparative analysis of elementary and realistic congestion control schemes on complex networks, highlighting the impact of network topology and algorithm choice on performance and bottleneck identification.

Findings

Proportional fairness and max-min fairness yield similar throughput but differ in flow inequality.

Scale-free networks show lower throughput in uniform-flow but higher in other algorithms depending on parameters.

The number of paths through an edge indicates bottleneck locations, linking network structure to congestion points.

Abstract

We consider two elementary (max-flow and uniform-flow) and two realistic (max-min fairness and proportional fairness) congestion control schemes, and analyse how the algorithms and network structure affect throughput, the fairness of flow allocation, and the location of bottleneck edges. The more realistic proportional fairness and max-min fairness algorithms have similar throughput, but path flow allocations are more unequal in scale-free than in random regular networks. Scale-free networks have lower throughput than their random regular counterparts in the uniform-flow algorithm, which is favoured in the complex networks literature. We show, however, that this relation is reversed on all other congestion control algorithms for a region of the parameter space given by the degree exponent $\gamma$ and average degree ${k}$. Moreover, the uniform-flow algorithm severely underestimates the network throughput of congested networks, and a rich phenomenology of path flow allocations is only present in the more realistic $\alpha$-fair family of algorithms. Finally, we show that the number of paths passing through an edge characterises the location of a wide range of bottleneck edges in these algorithms. Such identification of bottlenecks could provide a bridge between the two fields of complex networks and congestion control.