On the Statistics of MFR Routing in One-Dimensional Ad Hoc Networks

The performance analysis of a wireless network significantly depends on the routing-related statistics. Power consumption, multihop communication delay, and position estimation are among the parameters that are affected by the routing scheme. In this paper, statistical parameters of the most forward within range routing in 1-D ad hoc networks are investigated. Several parameters, such as the probability mass function (pmf) of the number of broadcast hops, the probability density function of the connectivity distance for a given number of hops, and the pmf of the number of hops between the source and the destination, are derived. For cases where the exact analytical results are recursive and complicated, good approximate nonrecursive formulas are also derived. We verify the correctness of the exact formulas and the precision of the approximate results by simulations. Some applications of the derived statistical parameters are also presented.