Robot-based compact storage and retrieval systems (RCSRS) have seen many implementations over the last few years. In such a system, the inventory items are stored in bins, organized in a grid. In each cell of the grid, a certain number of bins are stored on top of each other. Robots with transport and lifting capabilities move on the grid roof to transport bins between manual workstations and storage stacks. We estimate performance and evaluate storage policies of RCSRS, considering both dedicated and shared storage policies coupled with random and zoned storage stacks. Semi-open queueing networks (SOQNs) are built to estimate the system performance, which can handle both immediate and delayed reshuffling processes. We approximate the models by reduced SOQNs with two load-dependent service nodes and use the Matrix-Geometric Method (MGM) to solve them. Both simulations and a real case are used to validate the analytical models. Assuming a given number of stored products, our models can be used to optimize not only the length to width ratio of the system, but also the stack height, depending on the storage strategy used. For a given inventory and optimal system configuration, we demonstrate that the dedicated storage policy outperforms the shared storage policy in terms of dual command throughput time. However, from a cost perspective, wit
