Cost/speed analysis of mobile wireless DTNs under random waypoint mobility

We study a wireless network comprising an infinite number of nodes moving in ℝ
²
according to a Random Waypoint (RWP) mobility model. Each node is equipped with a radio transceiver with transmission range R; a transmission across a distance d incurs a quadratic cost d
²
. We assume that a packet is generated at one node and must be delivered to a destination located at an infinite distance in the direction of the positive x-axis through a combination of wireless transmissions and physical transports on the buffers of nodes. A routing rule specifies when a wireless transmission should take place. Given this setting, we develop an analytic framework, using tools from stochastic geometry and Markov chains theory, to evaluate, with certain approximations, the tradeoff between the speed with which the packet travels toward the destination and the transmission cost incurred per unit of distance. Simulation results show a good match with the analytical results.