Path selection in mobile ad-hoc networks and distribution of path duration

We investigate the issue of path selection in mobile multi-hop wireless networks. We are interested in designing a path selection algorithm that maximizes the expected duration of the selected path. To this end we first study the distribution of path duration. We show that, under a set of mild conditions, when the hop count along a path is large, the distribution of path duration can be well approximated by an exponential distribution even when link durations are dependent and their distributions are heterogeneous. Second, we investigate the relation between a path duration and durations of the links along the path. We prove that the parameter of the exponential distribution, which determines the expected duration of the path, is related to the link durations only through their means and is given by the sum of the inverses of the expected link durations. We validate our analytical results using ns-2 simulation with the Random Waypoint and Manhattan mobility models.