The rack-moving mobile robot (RMMR) system is a special parts-to-picker automated warehousing system that uses hundreds of rack-moving machines to accomplish the repetitive tasks of storing and retrieving parts by lifting and transporting unit racks autonomously. This paper investigates the operation cycle of the rack-moving machine for storage and retrieval from the perspective of the lane depth, especially exploring the particularity of the RMMR system in multi-deep lanes, and proposes expected travel time models of the rack-moving machine for single- and multi-deep layouts of the RMMR system. To validate the effectiveness of the proposed models, an experimental simulation was conducted with a 1–4-deep layout under six scenarios of different numbers of aisles and layers, and results were compared with results obtained using proposed models. The paper presents useful guidelines for the configuration of the RMMR system layout including the determination of the optimal lane depth.