Controlling Congestion on Complex Networks

From the Internet to road networks and the power grid, modern life depends on controlling flows on critical infrastructure networks that often operate in a congested state. Yet, we have a limited understanding of the relative performance of the control mechanisms available to manage congestion and of the interplay between network topology, path layout and congestion control algorithms. Here, we consider two flow algorithms (max-flow and uniform-flow), and two more realistic congestion control schemes (max-min fairness and proportional fairness). We analyse how the algorithms and network topology affect throughput, fairness and the location of bottleneck edges. Our results show that on large random networks a network operator can implement the trade-off (proportional fairness) instead of the fair allocation (max-min fairness) with little sacrifice in throughput. We illustrate how the previously studied uniform-flow approach leaves networks severely underutilised in comparison with congestion control algorithms, and how uniform-flow can (erroneously) lead to the conclusion that ER networks are more efficient than SF at the onset of congestion. For proportional fairness and max-min fairness, we found that SF networks are more unequal than ER. Finally, we found that links with high edge betweenness centrality are good candidates for bottleneck edges.