Connectivity in ad-hoc and hybrid networks

Abstract

Abstract-We consider a large-scale wireless network, but with a low density of nodes per unit area. Interferences are then less critical, contrary to connectivity. This paper studies the latter property for both a purely ad-hoc network and a hybrid network, where fixed base stations can be reached in multiple hops. We assume here that power constraints are modeled by a maximal distance above which two nodes are not (directly) connected.We find that the introduction of a sparse network of base stations does significantly help in increasing the connectivity, but only when the node density is much larger in one dimension than in the other. We explain the results by percolation theory. We obtain analytical expressions of the probability of connectivity in the 1-dim. case. We also show that at a low spatial density of nodes, bottlenecks are unavoidable. Results obtained on actual population data confirm our findings.

Modeling Sensor Networks

“…However, inspired by percolation theory, also Poisson models have been proposed [29]; thus, the positions of the nodes are distributed in R 2 according to a homogeneous Poisson point process of constant density λ per unit area.…”

Connectivity in one-dimensional ad hoc networks: A queueing theoretical approach

“…Denoting by P t x the transmission power, we find that two nodes may communicate with each other if their distance is less than or equal to the communication range R = P tx P noise 1 α . In such a situation it is a well known result that, for any finite R, the resulting network will be disconnected P-almost surely [3]. Furthermore, the network will be P-almost surely divided into an infinite number of finite clusters, which will be referred to in the following as "spatial clusters".…”

“…Then, evaluation of p C (d) may be performed integrating (8), leading to the formula obtained in [3] solving a differential equation with appropriate boundary conditions. In Fig.…”

“…The growing interest in the field of self-organizing wireless networks, often referred to as ad hoc, has led to a considerable amount of literature dealing with the characterization of the limiting performance of such networks, in terms of both connectivity [1][2][3][4] and capacity [5][6][7][8][9][10], two intimately related issues [11]. In this paper, we focus on one-dimensional ad hoc networks, in which nodes are randomly deployed over an infinite line, and present novel results on connectivity and coverage.…”

“…In the literature, results for the connectivity of onedimensional networks are presented in [2,3,12,13]. In all these papers, the nodes are assumed to be distributed according to either a uniform or a Poisson distribution on an infinite line.…”