The stocker system is another name of automated storage and retrieval system (AS/RS) and being popularly used as main material handling tools in Liquid Crystal Display (LCD) and semiconductor fabrication facilities. Recently the use of the stocker system has been extended to transportation from conventional storage and retrieval in LCD fabrication facilities. Toolsets are connected in the ground level of the stocker system and 4~6 stories of the shelves are placed in the upper or lower ground level. As a consequence of the more sophisticated design, move requests imposed on the system greatly increased. For solving this problem, the industry adopted the dual-robot stocker system that two robots are moving along the same guide line in the stocker system. This research develops a closed-form solution to estimate a delivery rate of the dual robot stocker system under given design and operation parameters. Using this stochastic model, industry practitioners could analyze performance levels under given various design parameters, and ultimately the model helps optimizing the design parameters.