Modeling urban road networks

According to New Scientist, two physicists from France and the U.S. have developed a simple mathematical model which shows how urban road networks evolve. Their model shows that urban street patterns and leaf pattern formation follow similar rules. The researchers validated their theoretical model by analyzing real road networks in about 300 cities. They've looked at young cities, such as Brasilia, and older ones, such as Cairo or London. Their conclusion is that the evolution of urban road networks follows 'a simple universal mechanism despite significant cultural and historical differences.' But read more...

According to New Scientist, two physicists from France and the U.S. have developed a simple mathematical model which shows how urban road networks evolve. Their model shows that urban street patterns and leaf pattern formation follow similar rules. The researchers validated their theoretical model by analyzing real road networks in about 300 cities. They've looked at young cities, such as Brasilia, and older ones, such as Cairo or London. Their conclusion is that the evolution of urban road networks follows 'a simple universal mechanism despite significant cultural and historical differences.' But read more...

Evolution of a urban road network

You can see above some snapshots of the evolution of a urban road network through time. "Examples of patterns obtained for a spatially uniform distribution of new centers are shown for different times. As time progresses, density increases, and the typical length from a center to the existing road network shortens as observed in the simulations." (Credit:IU)

This research work has been conducted by two physicists. Marc Barthelémy, of the French Atomic Energy Commission is currently a Visiting Faculty Scholar at Indiana University (IU) in the U.S. He worked on this project with Alessandro Flammini, Assistant Professor of Informatics at IU.

Here is an excerpt of the New Scientist article. "The main influence on the simulated network as it grows is the need to efficiently connect new areas to the existing road network -- a process they call 'local optimisation.' They say the road patterns in cities evolve thanks to similar local efforts, as people try to connect houses, businesses and other infrastructures to existing roads. Evolution has ensured that local efficiency also drives the growth of transport networks in biology -- for example, in plant leaf veins and circulatory systems.

According to the physicists, their model could help city planners to understand the evolution of street networks. "'Our study provides a first step in understanding and integrating such networks when modelling urban growth,' explains Flammini. The researchers will now study how road networks developed over time in old cities, such as London and Paris. They hope to unearth other possible universal features that might be present to refine their model."

This research work has been published in a recent issue of Physical Review Letters under the title "Modeling Urban Street Patterns" (Volume 100, Number 13, Article 138702, April 4, 2008). Here is a link to the abstract. "Urban street patterns form planar networks whose empirical properties cannot be accounted for by simple models such as regular grids or Voronoi tesselations. Striking statistical regularities across different cities have been recently empirically found, suggesting that a general and detail-independent mechanism may be in action. We propose a simple model based on a local optimization process combined with ideas previously proposed in studies of leaf pattern formation. The statistical properties of this model are in good agreement with the observed empirical patterns. Our results thus suggest that in the absence of a global design strategy, the evolution of many different transportation networks indeed follows a simple universal mechanism."

Thanks to arXiv.org, the full paper is available online (PDF format, 4 pages, 330 KB). The above figure and its caption have been extracted from this document.

Sources: Belle Dumé, New Scientist, April 23, 2008; and various websites

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