On the decentralized navigation of multiple packages on transportation networks
| Autor: | da Silva, Samuel M., Reis, Saulo D. S., Araújo, Ascânio D., Andrade, Jr, José S. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 98, 032306 (2018) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.98.032306 |
| Popis: | 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 $P(r_{ij})\sim r_{ij}^{-\alpha}$ [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, $p_{c}\sim L^{-\gamma}$, where $L$ is the network size. Our results indicate the presence of an optimal value of $\alpha_{\rm min}\approx1.7$, where the parameter $\gamma$ reaches its minimum value and the networks are more resilient to congestion for larger system sizes. Comment: 7 pages, 5 figures |
| Databáze: | arXiv |
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