Criticality of Large Delay Tolerant Networks via Directed Continuum Percolation in Space-Time

TL;DR

This paper analyzes the capacity of delay tolerant networks using directed continuum percolation theory, establishing conditions for network feasibility based on node density and mobility parameters.

Contribution

It introduces a novel percolation-theoretic framework for modeling DTN capacity with a specific mobility model and derives critical density thresholds.

Findings

DTN is feasible when mean node degree exceeds 4 e(g).

Derived numerical values for critical reduced number density e(g).

Analyzed asymptotic behavior of e(g) as g approaches infinity.

Abstract

We study delay tolerant networking (DTN) and in particular, its capacity to store, carry and forward messages so that the messages eventually reach their final destinations. We approach this broad question in the framework of percolation theory. To this end, we assume an elementary mobility model, where nodes arrive to an infinite plane according to a Poisson point process, move a certain distance L, and then depart. In this setting, we characterize the mean density of nodes required to support DTN style networking. In particular, under the given assumptions, we show that DTN is feasible when the mean node degree is greater than 4 e(g), where parameter g=L/d is the ratio of the distance L to the transmission range d, and e(g) is the critical reduced number density of tilted cylinders in a directed continuum percolation model. By means of Monte Carlo simulations, we give numerical values for e(g). The asymptotic behavior of e(g) when g tends to infinity is also derived from a fluid flow analysis.