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A model of urban scaling laws based on distance dependent interactions

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ABSTRACT

Socio-economic related properties of a city grow faster than a linear relationship with the population, in a log–log plot, the so-called superlinear scaling. Conversely, the larger a city, the more efficient it is in the use of its infrastructure, leading to a sublinear scaling on these variables. In this work, we addressed a simple explanation for those scaling laws in cities based on the interaction range between the citizens and on the fractal properties of the cities. To this purpose, we introduced a measure of social potential which captured the influence of social interaction on the economic performance and the benefits of amenities in the case of infrastructure offered by the city. We assumed that the population density depends on the fractal dimension and on the distance-dependent interactions between individuals. The model suggests that when the city interacts as a whole, and not just as a set of isolated parts, there is improvement of the socio-economic indicators. Moreover, the bigger the interaction range between citizens and amenities, the bigger the improvement of the socio-economic indicators and the lower the infrastructure costs of the city. We addressed how public policies could take advantage of these properties to improve cities development, minimizing negative effects. Furthermore, the model predicts that the sum of the scaling exponents of social-economic and infrastructure variables are 2, as observed in the literature. Simulations with an agent-based model are confronted with the theoretical approach and they are compatible with the empirical evidences.

No MeSH data available.


Histogram showing the number of amenities with a particular value of scaling exponent (βinfra). This histogram was built with 74 amenities (for instance, bakery (βinfra=0.847), beauty salon (=0.745), gas station (=0.652) and so on), all of them presenting scaling law with the population size, across 47 US cities. It is possible to note an evident sublinear scaling for all the amenities presented. The data used were collected directly from the references [31,32].
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RSOS160926F2: Histogram showing the number of amenities with a particular value of scaling exponent (βinfra). This histogram was built with 74 amenities (for instance, bakery (βinfra=0.847), beauty salon (=0.745), gas station (=0.652) and so on), all of them presenting scaling law with the population size, across 47 US cities. It is possible to note an evident sublinear scaling for all the amenities presented. The data used were collected directly from the references [31,32].

Mentions: Let us now focus on the infrastructure of the cities. In the present work, the focus is directed to the number of amenities a city has to offer. They are related to the infrastructure sector, and they usually present sublinear behaviour, as shown by figure 2. We built this histogram using 74 kinds of amenities (e.g. bakery (βinfra=0.847), beauty salon (=0.745), gas station (=0.652) and so on) across 47 US cities. The data were collected directly from the references [31,32], but other studies found similar results [9,29]. Although the model we present below relates to the number of amenities in a city, the framework must be valid to other infrastructure sectors of the city.Figure 2.


A model of urban scaling laws based on distance dependent interactions
Histogram showing the number of amenities with a particular value of scaling exponent (βinfra). This histogram was built with 74 amenities (for instance, bakery (βinfra=0.847), beauty salon (=0.745), gas station (=0.652) and so on), all of them presenting scaling law with the population size, across 47 US cities. It is possible to note an evident sublinear scaling for all the amenities presented. The data used were collected directly from the references [31,32].
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5383838&req=5

RSOS160926F2: Histogram showing the number of amenities with a particular value of scaling exponent (βinfra). This histogram was built with 74 amenities (for instance, bakery (βinfra=0.847), beauty salon (=0.745), gas station (=0.652) and so on), all of them presenting scaling law with the population size, across 47 US cities. It is possible to note an evident sublinear scaling for all the amenities presented. The data used were collected directly from the references [31,32].
Mentions: Let us now focus on the infrastructure of the cities. In the present work, the focus is directed to the number of amenities a city has to offer. They are related to the infrastructure sector, and they usually present sublinear behaviour, as shown by figure 2. We built this histogram using 74 kinds of amenities (e.g. bakery (βinfra=0.847), beauty salon (=0.745), gas station (=0.652) and so on) across 47 US cities. The data were collected directly from the references [31,32], but other studies found similar results [9,29]. Although the model we present below relates to the number of amenities in a city, the framework must be valid to other infrastructure sectors of the city.Figure 2.

View Article: PubMed Central - PubMed

ABSTRACT

Socio-economic related properties of a city grow faster than a linear relationship with the population, in a log–log plot, the so-called superlinear scaling. Conversely, the larger a city, the more efficient it is in the use of its infrastructure, leading to a sublinear scaling on these variables. In this work, we addressed a simple explanation for those scaling laws in cities based on the interaction range between the citizens and on the fractal properties of the cities. To this purpose, we introduced a measure of social potential which captured the influence of social interaction on the economic performance and the benefits of amenities in the case of infrastructure offered by the city. We assumed that the population density depends on the fractal dimension and on the distance-dependent interactions between individuals. The model suggests that when the city interacts as a whole, and not just as a set of isolated parts, there is improvement of the socio-economic indicators. Moreover, the bigger the interaction range between citizens and amenities, the bigger the improvement of the socio-economic indicators and the lower the infrastructure costs of the city. We addressed how public policies could take advantage of these properties to improve cities development, minimizing negative effects. Furthermore, the model predicts that the sum of the scaling exponents of social-economic and infrastructure variables are 2, as observed in the literature. Simulations with an agent-based model are confronted with the theoretical approach and they are compatible with the empirical evidences.

No MeSH data available.