Connectivity of Finite Wireless Networks with Random Communication Range Nodes

One of the most important topological characteristics of a network is its connectivity. This work analyzes the connectivity of one-dimensional wireless networks considering finite number of randomly deployed nodes with random communication ranges. In particular, it focuses on the probability of being able to convey a message from the source to the sink given certain number of nodes. The method to address the problem is by mapping it to the problem of covering a circle with arcs of random sizes. This paper provides an analytical solution when the communication ranges of the nodes are distributed uniformly over the field of interest. In addition, and of practical relevance, it shows how the random communication radii model can represent certain kind of randomness in the communication channel. Specifically there is a comparison between our model and the log-normal shadowing statistical model. Stochastic simulations validate the derived formula as well as its approximation to the standard shadowing model. In agreement to previous results for wireless networks, this work verifies that the requirements on the number of nodes to have a connected network may be relaxed when the nodes have random communication radii.