A Vertex Split-Recovery Model for Congestion Evolution Process on Road Networks

Functional failures are common phenomena in many flow-based complex networks, and pose significant impacts through disruptions in the system operations. We study a typical functional failure process - traffic congestion on... [ view full abstract ]

Functional failures are common phenomena in many flow-based complex networks, and pose significant impacts through disruptions in the system operations. We study a typical functional failure process - traffic congestion on urban road networks. Traffic congestion can be perceived as a form of temporal partial functional failure on road networks (road segments temporally closed or operating at a very inefficient level) due to high traffic load. Traditional approaches study the flow-induced functional failure processes by solving for flow patterns on networks using optimization-based methods, which detach functional properties from structural details. To model the traffic congestion process and incorporates the structural properties of real-world networks as well as realistic flow propagation characteristics, new analytical tools need to be developed in order to capture the non-trivial interactions between network structure and function

We develop a vertex split-recovery model for the traffic congestion evolution process on urban road networks. The model is built upon a functional dual representation of road networks. This dual representation represents intersections of road networks as dual edges, and merge the individual road segments into meaningful stretches of road and represent them as dual nodes based on axial direction and geometrical continuity. We show that under such representation, the traffic congestion/recovery on road segments is equivalent to the splitting/coalescing of dual nodes. This allows for converting a functional evolution process into an equivalent dynamic structural process, thereby enables jointly modeling of both structure and functional characteristics of the network. Congestion evolution data from two Chinese megacities (Beijing and Shanghai) are collected from a mainstream online digit map service and used to analyze the real-world vertex split-recovery process. We show that under congestion, the degree distribution of the functional dual network deviates from power law distribution (when no congestion present) towards a power law with exponential cutoff distribution. Numerical results show that the vertex split-recovery model well explains the observed congestion evolution process in both cities. We also successfully explained the emergence of the exponential cutoff behavior in the functional dual network and identified its relationship with the network loading level. Several topological (structural) features are found to have distinct impact on the emergence as well as the severity of congestion propagation. The vertex split-recovery model allows for analytically evaluating network functional performance under different network loading levels, which can serve a useful tool in better understanding and designing more resilient road networks.