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arXiv · 1806.06718

On the decentralized navigation of multiple packages on transportation networks

Samuel M. da Silva·Saulo D. S. Reis·Ascânio D. Araújo·José S. Andrade, Jr
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Abstract

We investigate by numerical simulation and finite-size analysis the impact of long-range shortcuts on a spatially embedded transportation network. Our networks are built from two-dimensional ($d=2$) square lattices to be improved by the addition of long-range shortcuts added with probability $P(r_{ij})\sim r_{ij}^{-α}$ [J. M. Kleinberg, Nature 406, 845 (2000)]. Considering those improved networks, we performed numerical simulation of multiple discrete package navigation and found a limit for the amount of packages flowing through the network. Such limit is characterized by a critical probability of creating packages $p_{c}$, where above this value a transition to a congested state occurs. Moreover, $p_{c}$ is found to follow a power-law, $p_{c}\sim L^{-γ}$, where $L$ is the network size. Our results indicate the presence of an optimal value of $α_{\rm min}\approx1.7$, where the parameter $γ$ reaches its minimum value and the networks are more resilient to congestion for larger system sizes.

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Samuel M. da Silva, Saulo D. S. Reis, Ascânio D. Araújo, José S. Andrade, Jr. 2018-06-15. On the decentralized navigation of multiple packages on transportation networks. https://doi.org/10.1103/physreve.98.032306

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