Adaptive schemes for estimating random graph parameters in mobile wireless ad hoc networks' modeling

To understand the complex behavior of a mobile ad hoc network, it is often necessary to proceed through the instantiation of a convenient theoretical model which can explain this behavior. The modeling tool we use in this paper is Erdös-Rényi approach. It emanate from random graph theory. Furthermore, since mobile wireless ad hoc and sensor networks are typically limited in memory resources and computational capacity, we develop an incremental algorithmic way to estimate parameters of such model and helps to a better understanding of the fundamental properties of the mobile wireless ad hoc networks' connectivity. To this end, we first focus on some basic formal concepts and notations from random graph theory, we relate the basic properties that describe mobile ad hoc networks and we study their connectivity by modeling the network as an undirected random graph. A particular attention is agreed for providing a computational framework for estimating model parameters in this context. Hence, using point estimation theory we show that it's possible to propose incremental schemes thus calculating efficiently the behavior model parameters. Since real implementations of ad hoc and sensor networks are expensive, the results presented in this paper are based on simulations of mobile ad hoc networks and analyzed with respect to the node degree variation.