A stochastic model to study the impact of the transmission frequency of hello messages on the connectivity of ad hoc networks

In this paper, we exploit the utility of Hello messages in the Ad hoc networks to study the impact of their transmission frequencies on the connectivity of the network. Assuming that the Hello messages arrive at a given node according to a Poisson process, we model a cluster-head motion (respectively an ordinary node motion) using a random process. This model allows us to find the critical value of the transmission frequency of Hello messages. We also have investigate a fundamental property of an Ad hoc network: its connectivity. We then analyze the number of neighbors of a given node, the isolation probability, the handoff probability and the probability that the considered network is connected, i.e. each node can communicate with an other node via the network.