Due to very expensive land cost in downtown area as well as increasing number of vehicles, the automated parking systems are becoming quite popular replacing traditional parking lots. Up to today, few researches are found in the literature which deals with the design problem of automated parking systems. In the thesis, a rotary parking system is studied which is known to be quite efficient in terms of space utilization. A expected service time model is proposed with an operating policy in which vehicle is stored at the closest open cage. The model is developed based on Markov process. The validity of the model is examined through a simulation study.