Performance analysis of automatic storage/retrieval systems by stochastic modelling

This study considers an automated storage/retrieval system that performs either single or dual commands and analyses it as a queuing system with two waiting spaces and one server. It is assumed that the storage and retrieval commands arrive at the system according to Poisson processes with different rates and that the service times of single and dual commands are distributed differently. The steady-state probability distribution of the number of commands in the system at the service completion epochs is derived; subsequently, the semi-Markov process is employed to obtain the distribution at an arbitrary time. Several performance measures are derived and include the expected number of commands in the system, the expected waiting time, the probability that an arbitrary command cannot enter the system (the ‘blocking probability’) and the utilization of the storage/retrieval machine.