Automated Storage and Retrieval Systems (AS/RSs) are an important facility for modern material management. The expected benefits of these capital-intensive facilities are gained when their control policies and their physical design parameters are determined simultaneously. In this paper we present several analytical models that capture the impact of the storage assignment policy and of the rack design on the expected storage and retrieval times. Sequential and interleaved service modes are considered for sequencing the storage and retrieval requests. We further investigate the impact of the rack structure on the relative performance of the following storage assignment policies : closest open location (random), full turnover-based policy, and class-based. Our analysis clearly indicates that significant savings in crane travel time are realized when implementing full turnover-based policy, rather than random. These savings become more and more pronounced as the profile of the storage racks approaches the square-in-time shape. Furthermore, it is shown that a class-based policy, with a small number of storage classes, will capture most of these savings and be easier to manage in practice.