Exact probability of connectivity one-dimensional ad hoc wireless networks

The probability that a one-dimensional stationary ad hoc wireless network is composed of at most C clusters is presented. The probability of network connectivity, i.e. the case of C=1, can be derived as a special case. A very simple approximate formula is also presented for the probability of network connectivity. We also explain our approximation heuristically, which confirms the analytical result. The analysis is validated by computing the probability of network connectivity and comparing it with the Monte Carlo simulation results.