Critical Transmitting Range for Biconnectivity of One-Dimensional Wireless Ad Hoc Networks

Abstract

Biconnectivity is the baseline graph theoretic metric of fault tolerance to node failures which can keep network connectivity while allowing unexpected node failures. In this paper we analyze this property for one-dimensional wireless Ad Hoc networks with finite nodes, which finds many applications in the real world, such as bus networks built along freeways and sensor networks deployed along frontiers. With common adopted assumption of uniform node distribution for static networks, the formula for the critical transmitting range that realizes network biconnectivity with certain probability is derived. Simulation results validate the accuracy of our conclusion and confirm its efficiency in practical network design.

A note on the 2-connectivity in one-dimensional ad hoc networks

“…Although Proposition 1 looks much more involved than eq. (16) in [12], our result holds accurately for all n, especially for small n, while eq. (16) is not applicable in this case.…”

“…Ref. [12] treats the 2-connectivity of G(n, z, r) under some asymptotical independence assumptions (see Remark 1 for a discussion).…”

“…In [12], Tian et al dealt with the probability of 2-connectivity for G(n, z, r) based on two independency approximation assumptions, which are validated by simulations when n is relatively large (e.g. n = 100).…”

Connectivity in a random interval graph with access points

“…In [1] the connectivity of G(n, z, r) with heterogeneous r is analyzed. [9,10] deal with the connectivity of G(n, z, r) involving some possible vertex failures. For more exact probabilities about connectivity and the number of components, see [4].…”