Policy-dependent multi-hop distances in linear ad hoc networks

In this paper we derive upper bounds on the multi-hop distributions of distances from a source to a destination N hops away yielding closed-form expressions for the average number of hops required to reach the given destination under different routing policies. Furthermore, we present a simple method to estimate the probability distribution P(NjD) of the number of hops given a certain Euclidean distance for each hopping strategy by using the results of the average number of hops. The results are useful to quantify the impact of hopping strategies on the performance and efficiency of multi-hop networks as well as to analyze the reliability in terms of delay and accuracy of certain applications such as flooding and localization.