Heavy traffic analysis of a single vehicle loop in an automated storage and retrieval system

We consider an automated storage/retrieval system in which cargo moves between the storage/retrieval machines and the system entrance/exit stations through a single automated vehicle loop. Past studies indicated that the cargo waiting time in the loop is affected by the dispatching rules, which govern the sequence of the cargo to be handled. In this paper, we show that the loop configuration, which has received little research attention, also has a big impact on the cargo waiting time. When the first-come-first-served dispatching rule is used, we derive the relationship between the number of stations and the ratio of the average cargo retrieval time to the average cargo storage time. When the first-encountered-first-served dispatching rule is used, we show that even the arrangement of the input channel and the output channel of a station can have significant impact on the cargo waiting time. Furthermore, we derive a formula for the vehicle visit rate for each station under heavy traffic conditions. This formula helps to explain the phenomenon that the waiting times at different stations can be very different even when the loop is symmetrically designed and the cargo arrival rates to the stations are similar. In addition to analytical models, we use simulations to evaluate the performance of different loop configurations. Our research suggests that a substantial improvement can be achieved by making proper adjustments to the loop configuration.