Continuum Percolation Threshold for Permeable Aligned Cylinders and Opportunistic Networking

We consider the critical percolation threshold for aligned cylinders, which provides a lower bound for the required node degree for the permanence of information in opportunistic networking. The height of a cylinder corresponds to the time a node is active in its current location. By means of Monte Carlo simulations, we obtain an accurate numerical estimate for the critical reduced number density, η_c≈0.3312(1) for constant height cylinders. This threshold is the same for all ratios of the height to the diameter of the base, and corresponds to the mean node degree of 1.3248 in opportunistic networking, which is clearly below the percolation threshold of 4.51 above which a gigantic connected component emerges in the network.