On the connectivity in one-dimensional ad hoc wireless networks with an access point

This paper investigates the connectivity in one-dimensional ad hoc wireless networks with an access point. We derive the probability that a random ad hoc wireless network has exactly m clusters by means of the methods of combinatorics and probability. The probability of connectivity, i.e. m = 1, can be obtained as a special case. Further, we explain how the transmission range of node affects the connectivity of the wireless network.