On k-connectivity for a geometric random graph
Random Structures & Algorithms
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks
IEEE Transactions on Mobile Computing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Combinatorics, Probability and Computing
The capacity of wireless networks
IEEE Transactions on Information Theory
Connectivity in obstructed wireless networks: from geometry to percolation
Proceedings of the fourteenth ACM international symposium on Mobile ad hoc networking and computing
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Connectivity properties of wireless networks in open space are typically modeled using geometric random graphs and have been analyzed in depth in different studies. Such scenarios, however, do not often represent situations encountered in practice, like urban environments or indoor spaces, which are deeply affected by obstacles. In this work, we present a model for obstructed wireless ad hoc networks consisting of a set of n nodes, deployed at random in a lattice square of size g×g, with a common transmission range r. For positioning the nodes in the field, all segments are considered as one-dimensional, but for communication purposes, we add a parameter µ to model the segments' width. Our model can be used to study the structure of obstructed networks analytically, as well as to simulate and evaluate a variety of node deployment strategies and the resulting network topologies. We derive analytical forms for the probability of existing crossing links between parallel and perpendicular segments sharing an intersection, toward a first topological characterization of our model. Moreover, we compute a lower bound for the probability of connectivity at intersections between segments, and apply percolation theory to derivate the Critical Transmission Range for connectivity in the overall network, i.e., the minimum transmission range that generates communication graphs that are connected with high probability.