Interleaving models for the analysis of twin shuttle automated storage and retrieval systems

A system of state equations is formulated for describing the dynamic behaviour of the queue of storage and retrieval transactions in a storage aisle served by twin shuttle storage and retrieval (S/R) machines. Using estimates of order picking cycle times in conjunction with storage and retrieval transaction demand levels, an estimate of the probability distribution of storage queue states is derived for a given storage aisle. System performance measures under an opportunistic interleaving discipline including S/R machine utilization, transaction queue lengths, average cycle times and expected transaction waiting times are approximated using the state probability distribution. The modelling tools are demonstrated using sample problems where the performance of twin versus single shuttle systems is contrasted for alternative combinations of storage and retrieval machine travel speeds, storage rack configurations, and transactions demand scenarios.