Distributed flow optimization and cascading effects in weighted complex networks

Abstract

We investigate the effect of a specific edge weighting scheme ∼ (kikj) β on distributed flow efficiency and robustness to cascading failures in scale-free networks. In particular, we analyze a simple, yet fundamental distributed flow model: current flow in random resistor networks. By the tuning of control parameter β and by considering two general cases of relative node processing capabilities as well as the effect of bandwidth, we show the dependence of transport efficiency upon the correlations between the topology and weights. By studying the severity of cascades for different control parameter β, we find that network resilience to cascading overloads and network throughput is optimal for the same value of β over the range of node capacities and available bandwidth.

Opening bottlenecks on weighted networks by local adaptation to cascade failures

“…Adapting into the equalized state may be useful in systems like communication networks and power grids, which must balance loads throughout the network [7, 8]. On communication networks, the equalized state can also aid in combating denial of service attacks.…”

“…Methods for identifying and widening bottlenecks have been developed in the context of communication networks and other engineering tasks [7–11]. These methods minimize bottlenecks by adopting an external, global point of view with complete knowledge and control of the network.…”

Structural robustness of scale-free networks against overload failures

“…In an actual network with overload failures, the failure of a node or an edge in the network often triggers successive failures of other elements, which constitutes a cascade of failures. The problem of cascading failures by overloads has been extensively studied so far [15][16][17][18][19][20][21][22][23][24][25]. These studies are based on many assumptions regarding the initial load, the load propagation process, the load distribution update method, etc.…”

“…This problem has been studied mainly in two contexts. One is related to the structural robustness argued in a percolation problem where a fixed number of nodes (or edges) are simultaneously removed [8][9][10][11][12][13][14] and the other is studied in a sense of the dynamical robustness against cascading failures in which the removal of a few nodes triggers the removal of remaining nodes [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. There have been a number of reports of the percolation problem on complex networks (i.e., structural robustness), particularly on scale-free networks with power-law degree distributions that are ubiquitous in real-world systems [7].…”

“…These examples show that overload failures are common origin of breakdowns of functional networks. Although overload failures have been studied extensively in the context of dynamical robustness against avalanchelike cascading failures [15][16][17][18][19][20][21][22][23][24][25], there is no work on the percolation transition induced by a simultaneous removal of overloaded nodes, which can form a basis of the study of cascading overload failures. Recently, Kishore et al examined the probability of a node having an overload failure as a function of the degree of the node [30,31].…”