The (max,+) theory allows to describe the behavior of Timed Event Graphs (TEG) with constant holding times. For time-varying systems, a class of First-In First-Out TEGs with periodic holding times has already been studied in the literature. We show here that such time-varying TEGs can be modeled by equivalent Weighted TEGs for which an input-output model exists. In summary, we can describe FIFO TEGs with periodic holding times by means of ultimately periodic formal series in a dioid denoted E * per δ .