Distributional convergence of path durations in MANETs with dependent link excess lives

We investigate the issue of path selection in multi-hop wireless networks with the goal of identifying a scheme that can select a path with the largest expected duration. 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 the distributions of link durations are dependent and heterogeneous. Secondly, we investigate the statistical relation between a path duration and the 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. Based on our analytical results we propose a scheme that can be implemented with existing routing protocols and select the paths with the largest expected durations