Connectivity of Large Wireless Networks Under A General Connection Model

@article{Mao2013ConnectivityOL,
  title={Connectivity of Large Wireless Networks Under A General Connection Model},
  author={Guoqiang Mao and Brian. D. O. Anderson},
  journal={IEEE Transactions on Information Theory},
  year={2013},
  volume={59},
  pages={1761-1772}
}
This paper studies networks where all nodes are distributed on a unit square <i>A</i>=<sup>Δ</sup> [- [1/2], [1/2]]<sup>2</sup> following a Poisson distribution with known density ρ and a pair of nodes separated by an Euclidean distance <i>x</i> are directly connected with probability <i>gr</i><sub>ρ</sub>(<i>x</i>)=<sup>Δ</sup><i>g</i>(<i>x</i>/<i>r</i><sub>ρ</sub>), independent of the event that any other pair of nodes are directly connected. Here, <i>g</i>:[0,∞)→ [0,1] satisfies the… 
Capacity of Large Wireless Networks with Generally Distributed Nodes
TLDR
A capacity upper bound is obtained for the capacity of a random network in which the nodes have a general spatial distribution and both bounds can be expressed as a product of four factors, which represents respectively the impact of node distribution, link capacity, number of source destination pairs and the transmission range.
Counting $k$ -Hop Paths in the Random Connection Model
TLDR
The mean and variance of the number of hop paths between two vertices in the random connection model, which is a random geometric graph where nodes connect probabilistically rather than deterministically according to a critical connection range, are studied.
Temporal connectivity in finite networks with non-uniform measures
TLDR
This work allows for insight into how non-uniformity (caused by mobility) and boundaries impact the connectivity features of temporal-spatial networks.
Connectivity of networks with general connection functions
TLDR
Here, the full connection probability of a dense network in a convex polygonal or polyhedral domain is expressed in terms of contributions from boundary components, for a very general class of connection functions.
Connectivity of Ad Hoc Wireless Networks with Node Faults
TLDR
This paper investigates the connectivity of random geometric graphs (RGGs) in the node fault model as an abstract model of ad hoc WSNs with unreliable nodes and provides two mathematical analyses: the asymptoticAnalysis for infinite RGGs that reveals the phase transition thresholds of connectivity, and the non-asymptotic analysis for finite RGGS that provides a useful approximation formula.
Connectivity and mobility in wireless networks
TLDR
This work uses a Poisson Point Process with non-uniform measure in some finite domain and model the links between points as probabilistic connection function to study a range of different networks even within the wireless communication literature, referred to as a Soft Random Geometric Graph.
Approximation Theory for Connectivity of Ad Hoc Wireless Networks With Node Faults
TLDR
The numerical results in Rayleigh MIMO model show that the approximation formula well estimates the connection probability even for finite graphs and that it provides useful information for design of WSN immune to node faults.
Optimal Radius for Connectivity in Duty-Cycled Wireless Sensor Networks
TLDR
It is proved that when the density of the nodes approaches infinity, then a finite component of size greater than 1 exists with probability 0 in this model and this result is used to obtain an optimal condition on node transmission radius that is both necessary and sufficient to achieve connectivity and is hence optimal.
A capacity upper bound for large wireless networks with generally distributed nodes
TLDR
The upper bound is shown to be tight in the sense that for the special case of networks with uniformly distributed nodes, the bound is in the same order as known results in the literature.
A New Measure of Wireless Network Connectivity
TLDR
It is demonstrated that the largest magnitude eigenvalue of the probabilistic connectivity matrix, which is positive, can serve as a good measure of the quality of network connectivity.
...
...

References

SHOWING 1-10 OF 31 REFERENCES
Connectivity of Large-Scale CSMA Networks
TLDR
It is shown that the transmission power only needs to be increased by a constant factor to combat interference and maintain connectivity compared with that considering a unit disk model (UDM) without interference.
On the asymptotic connectivity of random networks under the random connection model
TLDR
This paper analyzes the asymptotic distribution of the number of isolated nodes in the above network using the Chen-Stein technique and the impact of the boundary effect on the numberof isolated nodes as ρ → ∞ to derive a necessary condition for the abovenetwork to be asymPTotically almost surely connected.
Impact of interferences on connectivity in ad hoc networks
TLDR
It is proved that if /spl gamma/ is nonzero but small enough, there exist node spatial densities for which the network contains a large (theoretically infinite) cluster of nodes, enabling distant nodes to communicate in multiple hops.
Critical Power for Asymptotic Connectivity in Wireless Networks
In wireless data networks each transmitter's power needs to be high enough to reach the intended receivers, while generating minimum interference on other receivers sharing the same channel. In
Asymptotic distribution of the number of isolated nodes in wireless ad hoc networks with Bernoulli nodes
TLDR
A probabilistic study of the connectivity of wireless ad hoc networks containing inactive nodes, which shows that if all nodes have a maximum transmission radius r/sub n/=/spl radic/(lnn+/spl xi/)//spl pi/pn for some constant / spl xi/, then the total number of isolated nodes is asymptotically Poisson with mean e/sup -/spl Xi//.
Asymptotic distribution of the number of isolated nodes in wireless ad hoc networks with Bernoulli nodes
TLDR
A probabilistic study of the connectivity of wireless ad hoc networks containing inactive nodes and it is shown that if all nodes have a maximum transmission radius r/sub n/ = /spl radic/(ln n+c//spl pi/pn) for some constant c, then the total number of isolated nodes is asymptotically Poisson with mean e/sup -c/ and the totalNumber of isolated active nodes is also asymptonetically Poisson.
Towards a Better Understanding of Large-Scale Network Models
TLDR
Through two case studies related to network connectivity on the expected number of isolated nodes and on the vanishing of components of finite order respectively, some subtle but important differences are demonstrated between the infinite network model and the dense and extended network models.
Connectivity of wireless multihop networks in a shadow fading environment
TLDR
A tight lower bound for the minimum node density that is necessary to obtain an almost surely connected subnetwork on a bounded area of given size is given.
Stochastic geometry and random graphs for the analysis and design of wireless networks
TLDR
This tutorial article surveys some of these techniques based on stochastic geometry and the theory of random geometric graphs, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature.
The Number of Neighbors Needed for Connectivity of Wireless Networks
TLDR
It is shown that in a network with n randomly placed nodes, each node should be connected to Θ(log n) nearest neighbors, and it appears that the critical constant may be close to one, but that remains an open problem.
...
...