We report on a data-driven investigation aimed at understanding the dynamics of message spreading in a real-world dynamical network of human proximity. We use data collected by means of a proximity-sensing network of wearable sensors that we deployed at three different social gatherings, simultaneously involving several hundred individuals. We simulate a message spreading process over the recorded proximity network, focusing on both the topological and the temporal properties. We show that by using an appropriate technique to deal with the temporal heterogeneity of proximity events, a universal statistical pattern emerges for the delivery times of messages, robust across all the data sets. Our results are useful to set constraints for generic processes of data dissemination, as well as to validate established models of human mobility and proximity that are frequently used to simulate realistic behaviors.
Human trajectories are often approximated by random walk models. Measurements suggest that animal but also human trajectories can be approximated by L ' e vy flights @cite_15 @cite_3 @cite_13 @cite_33 . Mobility patterns of individuals at the geographic scale, as obtained from mobile phones, show that the distribution of displacements over all users is well approximated by a truncated power-law @cite_27 . Investigating mobility at the geographic scale, however, does not shed light on the shorter-range scale that is relevant for individual mobility and proximity in contexts that are relevant for data diffusion and its applications.
@cite_33 @cite_3 @cite_27 @cite_15 @cite_13
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There is substantial interest in the effect of human mobility patterns on opportunistic communications. Inspired by recent work revisiting some of the early evidence for a L´evy flight foraging strategy in animals, we analyse datasets on human contact from real world traces. By analysing the distribution of inter-contact times on different time scales and using different graphical forms, we find not only the highly skewed distributions of waiting times highlighted in previous studies but also clear circadian rhythm. The relative visibility of these two components depends strongly on which graphical form is adopted and the range of time scales. We use a simple model to reconstruct the observed behaviour and discuss the implications of this for forwarding efficiency. 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. This study used a sample of 100,000 mobile phone users whose trajectory was tracked for six months to study human mobility patterns. Displacements across all users suggest behaviour close to the Levy-flight-like pattern observed previously based on the motion of marked dollar bills, but with a cutoff in the distribution. The origin of the Levy patterns observed in the aggregate data appears to be population heterogeneity and not Levy patterns at the level of the individual. Newtonian physics began with an attempt to make precise predictions about natural phenomena, predictions that could be accurately checked by observation and experiment. The goal was to understand nature as a deterministic, “clockwork” universe. The application of probability distributions to physics developed much more slowly. Early uses of probability arguments focused on distributions with well‐defined means and variances. The prime example was the Gaussian law of errors, in which the mean traditionally represented the most probable value from a series of repeated measurements of a fixed quantity, and the variance was related to the uncertainty of those measurements. 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].