On the Levy-Walk Nature of Human Mobility

Abstract

We report that human walks performed in outdoor settings of tens of kilometers resemble a truncated form of Levy walks commonly observed in animals such as monkeys, birds and jackals. Our study is based on about one thousand hours of GPS traces involving 44 volunteers in various outdoor settings including two different college campuses, a metropolitan area, a theme park and a state fair. This paper shows that many statistical features of human walks follow truncated power-law, showing evidence of scale-freedom and do not conform to the central limit theorem. These traits are similar to those of Levy walks. It is conjectured that the truncation, which makes the mobility deviate from pure Levy walks, comes from geographical constraints including walk boundary, physical obstructions and traffic. None of commonly used mobility models for mobile networks captures these properties. Based on these findings, we construct a simple Levy walk mobility model which is versatile enough in emulating diverse statistical patterns of human walks observed in our traces. The model is also used to recreate similar power-law inter-contact time distributions observed in previous human mobility studies. Our network simulation indicates that the Levy walk features are important in characterizing the performance of mobile network routing performance.

Exploration–exploitation trade-off features a saltatory search behaviour

“…Foraging movement patterns that fit closely to walks (1.1) known as Lévy flights [7] were identified in many living spieces ranging from micro-organisms to humans [4][5][6][8][9][10][11][12][13][14][15][16][17][18][19][20], although the reported scaling exponents varied substantially for different animals, in different environmental contexts. The rate of flight lengths decay in the population data is typically described by a power law with an exponential cut-off revealing that an exponential decay rate dominates for extremely long travels [13,21].…”

“…The analysis of adaptive strategies instantaneously evolving in VE accentuates the key biological mechanisms of searching behaviour more vividly than the analysis of empirical data recorded in situ. Furthermore, in VE, we can study the mobility patterns of humans with extremely high resolution, up to the scales of millimetres and milliseconds, obtaining by far the most accurate data virtually comparable to either the scales of a few meters/tenth of seconds, kilometres per hours (in GPS tracking data; [19]), or the scale of a few thousand kilometres per week (in banknote travel patterns; [11]) discussed in the previous studies.…”

Onset of anomalous diffusion from local motion rules

“…Among these unusual diffusion processes, Lévy flights have been extensively studied on lattices and continuous media [1,2] as they can display superdiffusion, so that the variance of the distance covered during the process grows superlinearly x 2 (t) ∝ t γ with γ > 1 at odds with linear diffusion for the Brownian motion [3,4]. This enhanced diffusion entails an efficient exploration of the space in which the diffusion process takes place: thus both in natural contexts and in artificial ones Lévy flights have emerged as a strategic choice for such an exploration and for search strategies [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. In the case of Lévy flights, the whole process relies on the divergence of the second moment of the jump probability distribution P ( ), i.e.…”

Energy-aware collaborative sensing for multiple applications in mobile cloud computing

“…Here we relax that assumption and update our algorithm specification to include a prediction of the mobile device locations based on a model of human mobility patterns. Gonzalez et al [12] have shown that human mobility can be compared to a Levy walk with heavy-tail flight distribution and Rhee et al [13] have presented a truncated Levy walk model for the same. We use this truncated Levy walk mobility model for prediction of the mobile device locations.…”