Connectedness analysis of wireless relay placement with regular string topology by ordinary generating function

In a wireless ad hoc network, relays are used for passing the data from a source to a sink when the source is too far to reach the sink due to their transmission-range limitation. To evaluate the reliability of data transmission from source s to sink t, this paper proposes a mathematical analysis to calculate the probability of s-t connectedness when there can be failed relays. By using the technique of ordinary generating function, a closed-form solution has been obtained for wireless ad hoc networks with a regular string topology. Based on the obtained formula, numerical examples have been given and a network design paradox has been highlighted. Specifically, increasing the number of relays inappropriately in the wireless ad hoc network with regular string topology may even reduce the probability of s-t connectedness. Careful determination of regular relay placement, where the formula derived herein is applicable, can thus be of most useful in practice.