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.
Yoneki @cite_16 points out the importance of collecting real world data when modeling contact networks. Most available data sets that cover the short-range scale use Bluetooth or WiFi technologies to measure device proximity @cite_16 . @cite_24 extract mobility models from user traces, focusing on node localization and path tracing: the analyzed characteristics are node speeds and pause times that follow a log-normal distribution. @cite_5 present an experiment that involved about 40 participants at the Infocom 2005 conference, and report power-law distributions for the time intervals between node contacts.
@cite_24 @cite_5 @cite_16
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We examine the fundamental properties that determine the basic performance metrics for opportunistic communications. We first consider the distribution of inter-contact times between mobile devices. Using a diverse set of measured mobility traces, we find as an invariant property that there is a characteristic time, order of half a day, beyond which the distribution decays exponentially. Up to this value, the distribution in many cases follows a power law, as shown in recent work. This powerlaw finding was previously used to support the hypothesis that inter-contact time has a power law tail, and that common mobility models are not adequate. However, we observe that the time scale of interest for opportunistic forwarding may be of the same order as the characteristic time, and thus the exponential tail is important. We further show that already simple models such as random walk and random way point can exhibit the same dichotomy in the distribution of inter-contact time ascin empirical traces. Finally, we perform an extensive analysis of several properties of human mobility patterns across several dimensions, and we present empirical evidence that the return time of a mobile device to its favorite location site may already explain the observed dichotomy. Our findings suggest that existing results on the performance of forwarding schemes basedon power-law tails might be overly pessimistic. Characterizing the contacts between nodes is of utmost importance when evaluating mobile opportunistic networks. The most common characterization of inter-contact times is based on the study of the aggregate distribution of contacts between individual pairs of nodes, assuming an homogenous network, where contact patterns between nodes are similar. The problem with this aggregate distribution is that it is not always representative of the individual pair distributions, especially in the short term and when the number of nodes in the network is high. Thus, deriving results from this characterization can lead to inaccurate performance evaluation results.In this paper, we propose new approaches to characterize the inter-contact times distribution having a higher representativeness and, thus, increasing the accuracy of the derived performance results. Furthermore, these new characterizations require only a moderate number of contacts in order to be representative, thereby allowing to perform a temporal modelization of traffic traces. This a key issue for increasing accuracy, since real-traces can have a high variability in terms of contact patterns along time. The experiments show that the new characterizations, compared with the established one, are more precise, even using short time contact traces. With increasing prevalence of mobile wireless devices with WiFi and Bluetooth capability, new applications that can make use of limited contact opportunities when the devices are physically close are emerging. Proximity-based social networking, and location specific dissemination of advertisements and events, are some such applications. Discovering such services is a challenging problem due to energy budget limitations, user mobility, and nonuniformity and the time-varying nature of energy budgets across users. It is important to rapidly discover such mobile services to make use of limited contact opportunities. To support such applications, we seek to design a localized discovery scheme that can minimize the expected contact latency between mobile phones with limited energy budgets. All the existing neighbor discovery schemes assume lack of any time synchronization. However, in practice sufficiently accurate time synchronization can be achieved with existing time synchronization techniques. We propose Recursive Binary Time Partitioning (RBTP), a scheme that determines how the devices should wake up and sleep to achieve minimal contact latency with other nearby devices. RBTP achieves provable performance bound and outperforms state-of-the-art asynchronous protocols for smartphones. When compared with the optimum scheme, the contact latency is shown to be within a factor of (9 8) in the expected case and 2 in the worst case. Recent discovery of the mixture (power-law and exponential) behavior of inter-meeting time distribution of mobile nodes presents new challenge to the problem of mobility modeling and its effect on the network performance. Existing studies on this problem via the average inter-meeting time become insufficient when the inter-meeting time distribution starts to deviate from exponential one. This insufficiency necessarily leads to the increasing difficulty in the performance analysis of forwarding algorithms in mobile ad-hoc networks (MANET). In this paper, we analyze the effect of mobility patterns on the inter-meeting time distribution. We first identify the critical timescale in the inter-meeting distribution, at which the transition from power-law to exponential takes place, in terms of the domain size and the statistics of the mobility pattern. We then prove that stronger correlations in mobility patterns lead to heavier (non-exponential) 'head' of the inter-meeting time distribution. We also prove that there exists an invariance property for several contact-based metrics such as inter-meeting, contact, inter-any-contact time under both distance-based (Boolean) and physical interference (SINR) based models, in that the averages of those contact-based metrics do not depend on the degree of correlations in the mobility patterns. Our results collectively suggest a convex ordering relationship among inter-meeting times of various mobility models indexed by their degrees of correlation, which is in good agreement with the ordering of network performance under a set of mobility patterns whose inter-meeting time distributions have power-law 'head' followed by exponential 'tail'.