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A Parametric Description of Cities for the Normative Analysis of Transport Systems

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Abstract

Urban transport systems analysis requires some explicit or implicit representation of the network, activity pattern and flows pattern of the city. When dealing with transit design in real systems, detailed descriptions of cities are too complex to allow an analytical formulation that leads to exact results, so heuristics have been used. Alternatively, optimal design of transit systems at a strategic level has been done based on simplified descriptions using regular patterns or small networks to face and solve ad-hoc transit design problems. In this paper we propose a parametric description of cities for the normative analysis of transit systems. This is achieved after a synthesis of different ways to describe a city’s urban form that can be found in the literature, with an emphasis on the road network and the role of centers and subcenters. These diverse descriptions are assessed with the help of topological indicators and synthetic information regarding real cities. The parameters characterize the underlying network, the zones involved and the spatial pattern of transport demand, such that the design of public transport systems can be studied normatively for different city shapes. The model is applied to describe three very different real cities.

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Notes

  1. The most usual way to identify centers and subcenters is based on the activity pattern, but it is also possible to study the trip flows over the spatial network. For example, Zhong et al. (2014) identify the spots in the city that are more attractive when doing a random walk using probabilities associated to the observed flows. Louail et al. (2014) study the spatial concentration of mobile phones at different hours of the day in order to identify the evolution of hotspots.

  2. For the links between city form and the road network and its topology, see Barthélemy and Flammini (2009).

  3. In order to decide if two consecutive blocks are part of the same street, Porta et al. (2006b) and Lin and Ban (2013) show that a robust alternative is to define an angle close to 0° as the maximum acceptable difference between them.

  4. A graph is planar if it can be drawn in the plane without intersections between the arcs. In these graphs a “face” is an area surrounded by the arcs. A classic result shows that if n is the number of nodes and f the number of faces, then f will never be bigger than 2n-5 (Diestel 2000).

  5. A cycle in a graph is a path that starts and ends in the same node, without repeating any edge. A graph is called acyclic if it does not have cycles.

  6. Buhl et al. (2006), Hu et al. (2008) and Chan et al. (2011) study the average degree for several cities; Buhl et al. (2006) study the face coefficient; the average degree in the dual graph is studied by Jiang (2007), while the grid coefficient is studied by Figueiredo and Amorim (2007). The cluster coefficient is studied by Porta et al. (2006a, 2006b).

  7. With these definitions, the value of α for Mexico D.F. is 0.4 and less than 0.1 for Los Angeles, and the value of γ for Dallas-Fort Worth is 0.4 (see Fig. 1).

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Acknowledgments

This research was partially funded by Fondecyt, Chile, Grant 1160410, the Institute for Complex Engineering Systems (grants ICM: P-05-004-F and CONICYT: FBO16) and a Master Fellowship by CONICYT-Chile. Two unknown referees provided valuable comments.

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  1. Universidad de Chile, Casilla 228-3, Santiago, Chile

    Andrés Fielbaum, Sergio Jara-Diaz & Antonio Gschwender

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  1. Andrés Fielbaum
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Correspondence to Sergio Jara-Diaz.

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Fielbaum, A., Jara-Diaz, S. & Gschwender, A. A Parametric Description of Cities for the Normative Analysis of Transport Systems. Netw Spat Econ 17, 343–365 (2017). https://doi.org/10.1007/s11067-016-9329-7

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