Towards a dynamical model for wireless sensor networks

In this paper we introduce two dynamical models for a broadcast process in wireless sensor networks. We obtain a convergent martingale sequence for the two models. To our knowledge, such martingales were unknown previously. We look at the formal models using the formalisms of martingales, dynamical systems and Markov chains, each formalism providing complementary and coherent information with each other. The dynamics of both models are comparable and are validated in their domain of application with numerical simulation of wireless sensor networks. We make explicit the situations where the models are realistic. We also provide a formal analysis of the quasi-stationary distribution associated to the Markov chain corresponding to the second model proposed.