In multi-hop wireless networks, since source and destination nodes usually have some candidate paths between them, communication quality depends on the selection of a path from these candidates. For network design, characterizing the best path is important. To do this, in [1], [2], we used expected transmission count (ETX) as a metric of communication quality and showed that the best path for ETX is modeled by a path that consists of links whose lengths are close to each other in static one-dimensional multi-hop networks with a condition that the ETX function of a link is a convex monotonically increasing function. By using the results of this characterization, a minimum route ETX can be approximately computed in a one-dimensional random network. However, other metrics fail to satisfy the above condition, like medium time metric (MTM). In this paper, we use MTM as a metric of communication quality and show that we cannot directly apply the results of [1], [2] to the characterization of the best path for MTM and the computation of minimum route MTM. In this paper, we characterize the path that minimizes route MTM in a different manner from [1], [2] and propose a new approximate method suitable for the computation of minimum route MTM.