Percolation of heterogeneous flows uncovers the bottlenecks of infrastructure networks

Abstract

Whether it be the passengers’ mobility demand in transportation systems, or the consumers’ energy demand in power grids, the primary purpose of many infrastructure networks is to best serve this flow demand. In reality, the volume of flow demand fluctuates unevenly across complex networks while simultaneously being hindered by some form of congestion or overload. Nevertheless, there is little known about how the heterogeneity of flow demand influences the network flow dynamics under congestion. To explore this, we introduce a percolation-based network analysis framework underpinned by flow heterogeneity. Thereby, we theoretically identify bottleneck links with guaranteed decisive impact on how flows are passed through the network. The effectiveness of the framework is demonstrated on large-scale real transportation networks, where mitigating the congestion on a small fraction of the links identified as bottlenecks results in a significant network improvement.

Empirical evidence for a jamming transition in urban traffic

“…Cogani & Busonera [21,22] studied the spatial distribution of the clusters and found in agreement with Zhang et al [19] that, once formed, the clusters are stable in time, from day to day, indicating that their existence is determined by the traffic patterns (origins and destinations of the road users) and by the network itself. This approach opened new perspectives to analyse a road network, allowing in particular to identify the bottlenecks of the network, responsible for the collapse of the giant component into smaller clusters [23].…”

A reliability measure for smart surveillance systems

“…Hamedmoghadam et al [2] recently proposed a reliability measure for identifying bottlenecks in transportation networks. Their approach is based on a percolation model, in which each link (edge) in the network is associated with a link quality.…”

“…However, when performing percolation analysis on graphs representing real transport networks, Hamedmoghadam et al [2] notes that the critical threshold can be unclear. Hamedmoghadam et al instead focus on the unaffected demand that can be met by the network as ρ is varied.…”

“…In this paper, we present a reliability measure for smart surveillance systems, taking into account the adversarial nature of intrusion. Our approach is based on percolation theory which deals with the probability of a path emerging between two vertices in a graph or lattice, and is a generalisation of Hamedmoghadam et al's reliability measure, α [2].…”

Empirical evidence for a jamming transition in urban traffic

“…Cogani et al [21,22] studied the spatial distribution of the clusters and found in agreement with [19] that, once formed, the clusters are stable in time, from day to day, indicating that their existence is determined by the traffic patterns (origins and destinations of the road users) and by the network itself. This approach opened new perspectives to analyse a road network, allowing in particular to identify the bottlenecks of the network, responsible for the collapse of the giant component into smaller clusters [23].…”