Criticality condition for information floating with random walk of nodes

In an opportunistic content sharing system referred to as floating content, information is copied between mobile nodes upon node encounters inside an area which is called the anchor zone. We study the conditions under which information can be sustained in such a system. The anchor zone is assumed to be a circular disk, and a random walk type mobility model is adopted. First, we consider the one-speed case where all the nodes have a common velocity. Using the transport equation, adopted from nuclear reactor theory, we derive the criticality condition that defines a lower limit for the product of node density, communication distance and the radius of the anchor zone necessary 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 one-speed system, in general, the shape of the velocity distribution has an important effect: the higher the spread of the distribution, the lower the criticality threshold is. This effect is analyzed and discussed.