Probability Distribution of Multi-Hop Multipath connection in a Random Network

The aim of this paper is to verify that the convolution of the probability distribution of the link distance between any two nodes in a random network and the probability distribution of the number of hops required to establish a connection between the two nodes gives the connection probability between the two nodes. Such a connection probability obtained is for the best path in any multipath routing protocol. The paper also finds the probability of having at least one alternate path between the two nodes with two or more hops. All the mathematical formulations are validated with simulations.