Mobile ad hoc networks (MANETs) have inherently dynamic topologies. It is important to be able to determine the reliability of the communication paths created under these difficult circumstances. For this purpose, mobility metrics have been proposed in the literature, but most existing research is based on simulation results and empirical analysis. We consider two metrics, link persistence and path persistence, and develop an analytical framework to derive their exact expressions as well as the corresponding link residual time and path residual time, under a random mobility environment. Such exact expressions constitute precise mathematical relationships between the network connectivity and the mobility of mobile nodes. This framework could be used to develop efficient algorithms for medium access control, or to optimize existing network routing protocols.
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