It is discussed how to locate idle vehicles of AGVS on unidirectional guide paths. The problem is modeled as a median location problem on a cyclic network. The characteristics of the optimal location are analyzed and some useful properties are suggested to reduce the solution space. Based on the properties found, several special types of networks - a pure single-loop type, the loop type with a single branching intersection and the loop type with local branching node - are also analyzed as well as the general cyclic network. In each case of the networks, a solution procedure is suggested. Some numerical examples are provided to illustrate the algorithms developed.