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.

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.

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The routing performance of delay tolerant networks (DTN) is highly correlated with the distribution of inter-contact times (ICT), the time period between two successive contacts of the same two mobile nodes. As humans are often carriers of mobile communication devices, studying the patterns of human mobility is an essential tool to understand the performance of DTN protocols. From measurement studies of human contact behaviors, we find that their distributions closely resemble a form of power-law distributions called truncated Pareto. Human walk traces has a dichotomy distribution pattern of ICT; it has a power-law tendency up to some time, and decays exponentially after that time. Truncated Pareto distributions offer a simple yet cohesive mathematical model to express this dichotomy in the measured data. Using the residual and relaxation time theory [17] [4], we apply truncated Pareto distributions to quantify the performance of opportunistic routing in DTN. We further show that Truncated Levy walk (TLW) mobility model [22] commonly used in biology to describe the foraging patterns of animals [25], provide the same truncated power-law ICT distributions as observed from the empirical data, especially when mobility is confined within a finite area. This result confirms our recent finding that human walks contain similar statistical characteristics as Levy walks [22].