Percolation Transition in Simulated Urban Traffic

Urban traffic is known to undergo a phase transition when the total load is increased over some thresholdcite{Helbing2001}. A different kind of critical behavior is embodied by the percolation transition, recently demonstrated for real city trafficcite{Li2015}, in which the effective topology of the network is progressively fragmented by the emergence of bottleneck roads, unable to sustain traffic above some threshold speed. At criticality, the size distribution of the network's connected components follows a power law with a specific critical exponent that depends on the traffic regimecite{Zeng2019}. Here we present a model to simulate urban traffic over real, large-scale, full resolution (OpenStreetMap) networks. Our traffic model shares some ideas with Echenique et al.cite{Echenique2005}, but introduces the idea of vehicle probability density in place of explicit space-time trajectories and node queues. Real edge attributes such as length, direction and the number of lanes are taken into account. To model vehicle origins and destinations, we assume the urban population density to be locally proportional to network nodes over the map. Thus, traffic in our model is represented by a dynamic set of paths, one for each vehicle, starting from and terminating in uniformly random nodes. A new vehicle is added by associating it to the unweighted shortest path on a dynamic topology graph. Its edges are enabled (or disabled) depending on whether the number of existing paths sitting on them stays under (or above) a threshold. A path gets entirely removed from the network after a time proportional to its effective length $L$, which is equal to the geodetic distance $L_0$ multiplied by a slowdown factor derived from the fundamental traffic diagramcite{Helbing2001} of a typical city. Each edge has an independent slowdown factor proportional to the number of paths it hosts and to their length. Our method of traffic generation, while somewhat schematic, seems capable of capturing the salient properties of real-world phenomena and may be used to create extensive synthetic datasets for very large cities. Simulating the city of Beijing under increasing traffic conditions, we find multiple regimes for the critical exponent $tau$ for the percolation transition, as found by Zeng et al.cite{Zeng2019} by using GPS mobility data. Simulating an entire city network under a wide range of traffic conditions allows to better investigate theoretical questions and, for regulators, the possibility to improve city planning.

@Misc{CB19,
  author       = {Cogoni, M. and Busonera, G.},
  title        = {Percolation Transition in Simulated Urban Traffic},
  month        = {december},
  year         = {2019},
  type         = {Poster},
  keywords     = {traffic, urban networks, transport, simulation},
  url          = {https://publications.crs4.it/pubdocs/2019/CB19},
}