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.
Most analytical frameworks for message diffusion, such as Ref. @cite_25 are stochastic models used to compute message delay distributions based on parameters describing communication range and inter-contact time distributions, with no special characterization of the causal structure of message propagation. Other works such as Refs. @cite_17 and @cite_9 also focus on the analysis of the distributions of inter-meeting intervals.
@cite_9 @cite_25 @cite_17
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Numerous routing protocols have been proposed for Delay Tolerant Networking. One class of routing protocols aims at optimizing the delivery performance by using knowledge of previous encounters for forecasting the future contacts to determine suitable next hops for a given packet. Protocols pursuing such an approach face a fundamental challenge of choosing the right protocol parameters and the right time scale for estimation. These, in turn, depend on the mobility characteristics of the mobile nodes which are likely to vary within one scenario and across different ones. We characterise this issue, which has been overlooked in this field so far, using PROPHET and MaxPROP as two representative routing protocols and derive mechanisms to dynamically and independently determine routing parameters in mobile nodes. A stochastic model is introduced that accurately models the message delay in mobile ad hoc networks where nodes relay messages and the networks are sparsely populated. The model has only two input parameters: the number of nodes and the parameter of an exponential distribution which describes the time until two random mobiles come within communication range of one another. Closed-form expressions are obtained for the Laplace-Stieltjes transform of the message delay, defined as the time needed to transfer a message between a source and a destination. From this we derive both a closed-form expression and an asymptotic approximation (as a function of the number of nodes) of the expected message delay. As an additional result, the probability distribution function is obtained for the number of copies of the message at the time the message is delivered. These calculations are carried out for two protocols: the two-hop multicopy and the unrestricted multicopy protocols. It is shown that despite its simplicity, the model accurately predicts the message delay for both relay strategies for a number of mobility models (the random waypoint, random direction and the random walker mobility models). Inter-meeting time between mobile nodes is one of the key metrics in a Mobile Ad-hoc Network (MANET) and central to the end-to-end delay and forwarding algorithms. It is typically assumed to be exponentially distributed in many performance studies of MANET or numerically shown to be exponentially distributed under most existing mobility models in the literature. However, recent empirical results show otherwise: the inter-meeting time distribution in fact follows a power-law. This outright discrepancy potentially undermines our understanding of the performance tradeoffs in MANET obtained under the exponential distribution ofthe inter-meeting time, and thus calls for further study on the power-law inter-meeting time including its fundamental cause, mobility modeling, and its effect. In this paper, we rigorously prove that a finite domain, on which most of the current mobility models are defined, plays an important role in creating the exponential tail of the inter-meeting time. We also prove that by simply removing the boundary in a simple two-dimensional isotropic random walk model, we are able to obtain the empirically observed power-law decay of the inter-meeting time. We then discuss the relationship between the size of the boundary and the relevant time scale of the network scenario under consideration. Our results thus provide guidelines on the design of new mobility models with power-law inter-meeting time distribution, new protocols including packet forwarding algorithms, as well as their performance analysis.