Relaying in mobile ad hoc networks: The Brownian motion mobility model

Mobile ad hoc networks are characterized by a lack of a fixed infrastructure and by node mobility. In these networks data transfer can be improved by using mobile nodes as relay nodes. As a result, transmission power and the movement pattern of the nodes have a key impact on the performance. In this work we focus on the impact of node mobility through the analysis of a simple one-dimensional ad hoc network topology. Nodes move in adjacent segments with reflecting boundaries according to Brownian motions. Communications (or relays) between nodes can occur only when they are within transmission range of each other. We determine the expected time to relay a message and compute the probability density function of relaying locations. We also provide an approximation formula for the expected relay time between any pair of mobiles.