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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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). The dynamic behavior of the R-ALOHA packet broadcast system with multipacket messages is analyzed in this paper. It is assumed that each user handles one message at a time and the number of packets in a message is geometrically distributed. A Markovian model of the system is first formulated which explicitly contains the influence of the propagation delay of the broadcast channel. An approximate technique called equilibrium point analysis (EPA) is utilized to analyze the multidimensional Markov chain. The system stability behavior and the throughput-average message delay performance are demonstrated by the EPA. Numerical results from both analysis and simulation are given to assess the accuracy of the analytic results. Applying the analytic results to the slotted ALOHA with single packet messages, we prove mathematically that a method by Kleinrock and Lam for taking into account the influence of the propagation delay is an excellent approximation. In this paper, we develop a method for analyzing time-varying wireless channels in the context of the modern theory of the stochastic network calculus. In particular, our technique is applicable to channels that can be modeled as Markov chains, which is the case of channels subject to Rayleigh fading. Our approach relies on theoretical results on the convergence time of reversible Markov processes and is applicable to chains with an arbitrary number of states. We provide two expressions for the delay tail distribution of traffic transmitted over a fading channel fed by a Markov source. The first expression is tighter and only requires a simple numerical minimization, the second expression is looser, but is in closed form. We consider a channel model based on the diffusion of particles in the medium which is motivated by the natural communication mechanisms between biological cells based on exchange of molecules. In this model, the transmitter secretes particles into the medium via a particle dissemination rate. The concentration of particles at any point in the medium is a function of its distance from the transmitter and the particle dissemination rate. The reception process is a doubly stochastic Poisson process whose rate is a function of the concentration of the particles in the vicinity of the receiver. We derive a closed-form for the mutual information between the input and output processes in this communication scenario and establish useful properties about the mutual information. We also provide a signaling strategy using which we derive a lower bound on the capacity of the diffusion channel with Poisson reception process under average and peak power constraints. Furthermore, it is shown that the capacity of discretized diffusion channel can be a negligible factor of the capacity of continuous time diffusion channel. Finally, the application of the considered model to the molecular communication systems is discussed.