This thesis presents a stochastic analysis of a simplified end-of-aisle automatic storage and retrieval systems (AS/RS) using a queueing model with two linked queues. A simplified AS/RS with one storage rack, and one storage/retrieval (S/R) device of unit-load is considered. There are two queues, one of infinite capacity for the items waiting for storage and the other of finite capacity for the requests for items to be removed from storage based on the size of the storage rack. The S/R machine places them into storage and retrieves items on an alternating basis. Arrivals in both queues are assumed to follow a Poisson distribution, where the arrivals in the second queue are linked to the first queue. Service times of both queues follow an exponential distribution. A double-ended queueing model is developed and is studied as a Markov process. The resulting Markov chain is of the quasi-birth-and-death type. The Matrix-geometric approach is used to analyze this system and efficient algorithmic procedures for the computation of the rate matrix, steady state vector and important performance measures have been developed. Numerical examples are presented that show the behavior of the system for various rack sizes. As the rack size increases, the queue length and waiting time both decrease and system performance improves. However, it is shown that under certain conditions increasing the rack size gains minor improvements in system performance. The behavior of the system when jamming occurs is also discussed. (Abstract shortened by UMI.)