Modern cities encounter challenges related to parking scarcity arising from limited land space and congested traffic. Compact automated parking systems (CAPS) have gained increasing popularity in addressing this issue. These systems store cars in a multi-tier configuration and use a crane with a shuttle at the centre of the system to transport cars. The system throughput primarily relies on the configuration design and the control mechanisms of the crane and shuttle, which are established during the design phase and daily operations, respectively. Our study focuses on the dwell point, where the shuttle remains after completing a transaction, and the input/output (I/O) point. In contrast to existing studies, this paper considers two I/O points and the point-of-service-completion (POSC) dwell point policy. In this configuration, we develop both single-command (SC) and dual-command (DC) travel time models for CAPS with single and dual shuttles, respectively. Simulation is carried out to verify the accuracy of these models. We evaluate the effectiveness of the proposed policies and optimise the shape of CAPS. In addition, we numerically compare the retrieval time of single and dual shuttle systems, considering SC and DC. Our results show a critical ratio of shuttle travelling speed to the crane rotating speed exists. Beyond this ratio, the performance of single shuttle CAPS is better than that of dual shuttle CAPS, and the DC outperforming the SC in single shuttle CAPS. The results also indicate that DC always performs better in dual shuttle CAPS. Moreover, we compare our operating policies with those from previous studies and investigate the cost performance of our system. The results show the superiority of our policies and suggest their suitability for addressing diverse customer demands. Finally, we calculate the investment cost of single shuttle CAPS, and our system has a lower investment cost than traditional CAPS.
