This paper studies a robotic mobile fulfillment system (RMFS) featured by robots transporting movables shelves to order pickers. The RMFS can increase productivity, reduce costs, increase order picking accuracy, and improve operational flexibility. We build queue network models to describe the RMFS with two protocols in sharing robots for pickers, propose the corresponding algorithms, conduct numerical analyses, and evaluate the performance of the RMFS by calculating the throughput time. We then calculate the optimal number and the velocity of robots, and provide the effective design rules for the RMFS.