In many warehouses shuttle-based technologies have replaced the traditional AS/R system based storage technologies. The impact these systems have on downstream order picking performance is largely unknown. To study the interactions between upstream storage and downstream picking systems, we develop a novel analytical model for integrated storage and order picking systems. The resulting semi-open queuing model is solved using the matrix-geometric method. Using the queuing network model, we are able to study the effect of storage system technology on order throughput times, and the effect of the picking station input buffer size on order picking performance. Further, we analyze the effect of a constant work-in-process (CONWIP) control for orders on system performance. Our results indicate that using SBS/R instead of AS/R-based storage systems yields investment cost savings (i.e., fewer aisles in the storage area and fewer picking stations), paired with a lower total throughput time at a given order arrival rate. Numerical studies show how the total throughput time, first, benefits and then becomes stable by increasing the input buffer size at the picking stations. Retrieving item tote at the storage system in advance with respect to the picker availability is also advantageous, especially in the SBS/R system.