  As warehouses are emphasizing space utilization and the ability to handle
multi-line orders, multi-tote storage and retrieval (MTSR) autonomous mobile
robot systems, where robots directly retrieve totes from high shelves, are
becoming increasingly popular. This paper presents a novel shared-token,
multi-class, semi-open queueing network model to account for multi-line orders
with general distribution forms in MTSR systems. The numerical results obtained
from solving the SOQN model are validated against discrete-event simulation,
with most key performance metrics demonstrating high accuracy. In our
experimental setting, results indicate a 12.5% reduction in the minimum number
of robots needed to satisfy a specific order arrival rate using the closest
retrieval sequence policy compared with the random policy. Increasing the
number of tote buffer positions on a robot can greatly reduce the number of
robots required in the warehouse.
