Optimal transport in time-varying small-world networks
2016; American Physical Society; Volume: 93; Issue: 3 Linguagem: Inglês
10.1103/physreve.93.032321
ISSN2470-0061
AutoresChen Qu, Qian Jiang-Hai, Liang Zhu, Dingding Han,
Tópico(s)Stochastic processes and statistical mechanics
ResumoThe time-order of interactions, which is regulated by some intrinsic activity, surely plays a crucial role regarding the transport efficiency of transportation systems. Here we study the optimal transport structure by measure of the length of time-respecting paths. Our network is built from a two-dimensional regular lattice, and long-range connections are allocated with probability ${P}_{ij}\ensuremath{\sim}{r}_{ij}^{\ensuremath{-}\ensuremath{\alpha}}$, where ${r}_{ij}$ is the Manhattan distance. By assigning each shortcut an activity rate subjected to its geometric distance ${\ensuremath{\tau}}_{ij}\ensuremath{\sim}{r}_{ij}^{\ensuremath{-}C}$, long-range links become active intermittently, leading to the time-varying dynamics. We show that for $0<C<2$, the network behaves as a small world with an optimal structural exponent ${\ensuremath{\alpha}}_{\mathrm{opt}}$ that slightly grows with $C$ as ${\ensuremath{\alpha}}_{\mathrm{opt}}\ensuremath{\sim}log(C)$, while for $C\ensuremath{\gg}2$ the ${\ensuremath{\alpha}}_{\mathrm{opt}}\ensuremath{\rightarrow}\ensuremath{\infty}$. The unique restriction between $C$ and $\ensuremath{\alpha}$ unveils an optimization principle in time-varying transportation networks. Empirical studies on British Airways and Austrian Airlines provide consistent evidence with our conclusion.
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