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.
A wide range of commonly used models can be found in the survey about mobility models and ad-hoc networks by @cite_21 . The authors emphasize the need to devise accurate mobility models, and explore the limitations of current modeling strategies, pointing out that models with no memory (Random Walk and Random Waypoint) describe nodes whose actions are independent from one another. On the other hand, group mobility models, such as the Nomadic Community Mobility Model, aim at representing the behavior of nodes as they move together. @cite_3 model human contact networks using a generative model of human walk patterns based on L ' e vy flights, and reproduce the fat-tailed distribution of inter-contact times observed in empirical data of human mobility. This model is later used to characterize the routing performance in human-driven DTNs @cite_13 , predicting the message delivery ratio. No analysis is reported that takes into account the role of causality in the process of message diffusion based on these models.
@cite_21 @cite_13 @cite_3
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In the performance evaluation of a protocol for an ad hoc network, the protocol should be tested under realistic conditions including, but not limited to, a sensible transmission range, limited buffer space for the storage of messages, representative data traffic models, and realistic movements of the mobile users (i.e., a mobility model). This paper is a survey of mobility models that are used in the simulations of ad hoc networks. We describe several mobility models that represent mobile nodes whose movements are independent of each other (i.e., entity mobility models) and several mobility models that represent mobile nodes whose movements are dependent on each other (i.e., group mobility models). The goal of this paper is to present a number of mobility models in order to offer researchers more informed choices when they are deciding upon a mobility model to use in their performance evaluations. Lastly, we present simulation results that illustrate the importance of choosing a mobility model in the simulation of an ad hoc network protocol. Specifically, we illustrate how the performance results of an ad hoc network protocol drastically change as a result of changing the mobility model simulated. 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]. 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.