Connectivity Analysis of One-Dimensional Ad Hoc Networks with Arbitrary Spatial Distribution for Variable and Fixed Number of Nodes

In this paper, we propose an analytical approach to compute the probability of connectivity for one-dimensional ad hoc networks. The proposed analysis gives the exact probability of connectivity for an arbitrary distribution of nodes, provided that nodes are independently and identically distributed. We conduct separate analyses for two cases; in the first case, the number of nodes varies by time under a stationary distribution and in the second case, there is a fixed (known) number of nodes in the network. Using the approaches presented in this work, we are able to derive closed-form formulas for the probability of connectivity for some spatial distributions, while for more complicated distributions, our approach leads to tractable numerical algorithms. As an example, we apply our method to a special case (uniform distribution) and derive a closed-form formula for its probability of connectivity. Finally, we confirm the validity of our analytical approach by simulation for several distributions and show higher accuracy and applicability of the proposed approach compared with existing methods.