On the Connectivity of Ad Hoc Networks

@article{Bettstetter2004OnTC,
  title={On the Connectivity of Ad Hoc Networks},
  author={Christian Bettstetter},
  journal={Comput. J.},
  year={2004},
  volume={47},
  pages={432-447}
}
This paper presents a framework for the calculation of stochastic connectivity properties of wireless multihop networks. Assuming that n nodes, each node with transmission range r0, are distributed according to some spatial probability density function, we study the level of connectivity of the resulting network topology from three viewpoints. First, we analyze the number of neighbors of a given node. Second, we study the probability that there is a communication path between two given nodes… 
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References

SHOWING 1-10 OF 46 REFERENCES
On the minimum node degree and connectivity of a wireless multihop network
TLDR
This paper derives an analytical expression that enables the determination of the required range r0 that creates, for a given node density ρ, an almost surely k--connected network and investigates two fundamental characteristics of a wireless multi -hop network: its minimum node degree and its k--connectivity.
An evaluation of connectivity in mobile wireless ad hoc networks
  • P. Santi, D. Blough
  • Computer Science
    Proceedings International Conference on Dependable Systems and Networks
  • 2002
TLDR
The mobile version of the problem when d=2 is investigated through extensive simulations, which give insight on how mobility affects connectivity and reveal a useful trade-off between communication capability and energy consumption.
How to achieve a connected ad hoc network with homogeneous range assignment: an analytical study with consideration of border effects
  • C. Bettstetter, J. Zangl
  • Computer Science
    4th International Workshop on Mobile and Wireless Communications Network
  • 2002
TLDR
An analytical expression is derived that enables the determination of critical (r/sub 0/, n)-pairs that achieve, with high probability, a connected network in an area A, and the expected node degree and the probability that the network has no isolated node are calculated.
A probabilistic analysis for the range assignment problem in ad hoc networks
TLDR
A probabilistic solution to this range assignment problem achieves substantial energy savings and establishes lower and upper bounds on the probability of connectedness for the one-dimensional case.
Connectivity in ad-hoc and hybrid networks
TLDR
It is found 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.
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks
TLDR
The critical transmitting range for connectivity in wireless ad hoc networks is analyzed and insight into how mobility affects connectivity is yielded and useful trade offs between communication capability and energy consumption are revealed.
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.
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.
On the connectivity of wireless multihop networks with homogeneous and inhomogeneous range assignment
  • C. Bettstetter
  • Computer Science
    Proceedings IEEE 56th Vehicular Technology Conference
  • 2002
This paper investigates the connectivity of wireless multihop networks with uniformly randomly distributed nodes. We analyze the required transmission range that creates, for a given node density, an
Topology properties of Ad hoc networks with random waypoint mobility
TLDR
A closed-form approximation is derived for the critical (r0, n-pairs) that are needed to keep the mobile network connected during at least P(con)=99% of the time for a wireless multihop network with n nodes moving according to the random waypoint model.
...
...