Modelagem e análise de conectividade em redes sem fios obstruídas

Abstract

Connectivity properties of wireless networks in open space are typically modeled using geometric random graphs and have been analyzed in depth in di erent studies. Such scenarios, however, do not often represent situations encountered in practice, like urban environments or indoor spaces, which are deeply a ected by obstacles. As an alternative, we propose a model for obstructed wireless ad hoc networks consisting of a set of nodes deployed at random in a grid, all of them sharing a common transmission range. For positioning the nodes in the eld, all segments are considered as being one-dimensional, but for communication purposes, we add a parameter E to model the segments' width. We show how the resulting model can be used to study properties of such communication networks analytically and to simulate a variety of network topologies for performance evaluation of communication protocols in the aforementioned scenarios. In order to compute the probability of connectivity at segments' intersections (Pr(Icon)), we propose three di erent geometric models, namely, the Max-Norm, LoS and Triangular models. We show the diffculty of computing Pr(Icon) under the LoS, and we compute tight lower bounds for Pr(Icon) under the Max-Norm and Triangular models, with the respective upper bound of the approximation error. Additionally, we introduce an abstraction on the grid and apply percolation theory to compute the minimum transmission range that generates communication graphs that are connected with high probability (w.h.p.). The solution requires a minimal visibility at intersections, depending on the parameter E. We compute the minimal visibility required to have connectivity using the derived minimum transmission range. This particular transmission range is known as the CTR for connectivity, and we prove that the derived CTR for connectivity does not depends on the geometrical model at intersections. We performed a study of the scalability of obstructed networks within the proposed model and developed analytical methods to determine the possibility of obtaining connectivity w.h.p. in homogeneous topologies for speci c combinations of characteristics, e.g. segments' width, grid size and the maximum transmission range.