Modeling Hop Length Distributions for Reactive Routing Protocols in One Dimensional MANETs

In mobile ad hoc networks (MANETs), packets hop from a source to a series of forwarding nodes until they reach the desired destination. Defining the hop length to be the distance between two adjacent forwarding nodes, we observe that the two adjacent forwarding nodes tend to be farther away from each other with a higher probability in a one-dimensional MANET. We derive the probability density functions for the hop lengths to confirm our observation. Applying the developed results, we further formulate the relationship between the mean number of hops and the distance between the source and the destination.