Geographical networks evolving with an optimal policy

Xie, Yi; Zhou, Tao; Bai, Wen-Jie; Chen, Guanrong; Xiao, Wei-Ke; Wang, Bing–Hong

doi:10.1103/physreve.75.036106

Cited by 37 publications

(24 citation statements)

References 48 publications

(47 reference statements)

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“…On the other hand, if removals of facilities are allowed in addition, the upper points move to the lower part, making the scaling law D ∼ ρ α more visible. The difference in results comes from the presence of regulating processes such as removal or relocation, which are also shown in other studies of optimal networks (11,14,15).…”

Section: Summary and Discussionmentioning

confidence: 81%

Scaling laws between population and facility densities

Son

Lee

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

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When a new facility like a grocery store, a school, or a fire station is planned, its location should ideally be determined by the necessities of people who live nearby. Empirically, it has been found that there exists a positive correlation between facility and population densities. In the present work, we investigate the ideal relation between the population and the facility densities within the framework of an economic mechanism governing microdynamics. In previous studies based on the global optimization of facility positions in minimizing the overall travel distance between people and facilities, it was shown that the density of facility D and that of population ρ should follow a simple power law D ∼ ρ 2/3 . In our empirical analysis, on the other hand, the power-law exponent α in D ∼ ρ α is not a fixed value but spreads in a broad range depending on facility types. To explain this discrepancy in α, we propose a model based on economic mechanisms that mimic the competitive balance between the profit of the facilities and the social opportunity cost for populations. Through our simple, microscopically driven model, we show that commercial facilities driven by the profit of the facilities have α = 1, whereas public facilities driven by the social opportunity cost have α = 2/3. We simulate this model to find the optimal positions of facilities on a real U.S. map and show that the results are consistent with the empirical data.optimal positioning | social opportunity cost | microdynamics model

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Section: Summary and Discussionmentioning

confidence: 81%

Scaling laws between population and facility densities

Son

Lee

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

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show abstract

“…In the spatial or geographical networks [33,34], the cost of establishing long-range connections between distant spots is usually higher than the cost of establishing short-range connections. This is clear for railway network, where establishing a long-range connection is obviously expensive because long channels need a larger infrastructure.…”

Section: The Geographical Constraint Of Networkmentioning

confidence: 99%

Geographic coarse graining analysis of the railway network of China

Wang

Jiang-Xia

Wang

et al. 2008

Physica A: Statistical Mechanics and its Applications

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“…What are the key factors that lead the cortical networks to small-world graphs? Some recent works have demonstrated that the spatially preferential attachment mechanism plays a major role in determining the network evolution [15][16][17][18]. Since these models embrace the topologically preferential attachment introduced by Barabsi and Albert [19], it would result in the fact that the nodes added to the network in the early time have larger probability to become the highly connected ones.…”

Section: Introductionmentioning

confidence: 99%