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  1. J. Virtamo, E. Hyytiä and P. Lassila, Criticality Condition for Information Floating with Random Walk of Nodes, Performance Evaluation, vol. 70, no. 2, pp. 114-123, 2013 (link)(bib)
    Abstract: The conditions under which information can be sustained in an opportunistic content sharing system are studied. The anchor zone is assumed to be a circular disk, and a random walk type mobility model is adopted. First, the 1-speed case with all the nodes having a common velocity is analyzed. Using the transport equation, adopted from nuclear reactor theory, the criticality condition is derived, defining a lower limit for the product of node density, communication distance and the radius of the disk for information floating. The dependence of this criticality parameter on the mean step size of the random walk is numerically established. Complemented by the asymptotic behavior, found by diffusion theory, an accurate approximation formula is derived. While the velocity of the nodes does not appear at all in the criticality condition of the 1-speed system, in general, the shape of the velocity distribution has an important effect: the higher the spread of the distribution, the lower is the criticality threshold. This effect is analyzed and discussed.