Stochastic model for the characterization of a cluster and its resources in an ad-hoc network

One of the expected properties of the ad hoc networks is the ability to increase its size to receive new nodes and configure new applications without affecting the quality of services. This property, called scalability is affected by the decentralized nature of ad hoc networks making it necessary to develop mechanisms that allow a large number of nodes work together without affecting network performance. In this paper, we propose a stochastic model based on the geometric distribution, which allows to characterize the level of resources in a hierarchical architecture and then establish an appropriate relationship between the level of resources of two successive layers of the network.