A unit-load automated guided vehicle system is considered in which a single vehicle is operated on a unidirectional path in a closed loop. The vehicle serves a manufacturing cell moving pallets from one station to another based on the "First-Encountered-First-Serve" dispatching rule. An approximation method is developed to compute the mean waiting time of an arbitrary pallet at each station. Extensive numerical experiments, performed for various problems, yield fairly good results in most of the cases compared with those obtained by simulation method.