Mean free path applied to message dissemination in opportunistic networks

Opportunistic networking including Delay-/Disruption-Tolerant Networking (DTN) has become an increasingly real possibility since there are a huge number of mobile devices, such as smartphones, all over the world. DTN is expected to find promising applications, such as message dissemination in a disaster-struck area, and offloading mobile data traffic onto DTNs in urban areas. One of the potential issues that may confront these applications is that opportunities for message relaying are limited since smartphone users are sparsely distributed among base station cells. In order to disseminate message efficiently, it is important to be able to accurately evaluate DTN performance, such as message dissemination coverage, and time. In this paper, we propose a novel yet simple analytical model of message dissemination in DTNs by applying the concept of mean free path. The mean free path is the average distance that a particle (e.g., an atom or a molecule) travels between successive collisions (in physics jargon). The basic idea is that by mapping a particle in three-dimensional space to a node in two-dimensional space, a meeting between two nodes is represented as a collision between two particles. We also perform simulation experiments in order to validate our model.