Analytical approach of merging a different number of storage aisle under a fully sequenced order

This paper presents a method to determine the throughput of a multiple-aisle storage system. The main key feature of this approach is that the sequence of the ordered order is to be strictly adhered and the buffer-slots in front of every storage aisle are considered. Therefore, a merging process with several input streams with limited capacity is modelled. The invented approach is based on a superposition of different queueing systems with limited capacity, such as a M/M/1/K-queueing model. The accuracy of the invented approach is given by a comparison to a discrete event simulation. The approximation quality is very high, through an estimation error of less than 10% for some configurations and less than 2% for over 90% of all examined configurations. An example is presented to show the influence of the number of aisles and their capacity. The result is that the capacity of the aisle has a prime influence on the throughput, especially at a higher number of aisles. This approach serves a decision tool to determine the throughput of a multi-aisle storage system in an accurate and a simple manner.