  In the contemporary logistics industry, automation plays a pivotal role in
enhancing production efficiency and expanding industrial scale. Autonomous
mobile robots, in particular, have become integral to the modernization efforts
in warehouses. One noteworthy application in robotic warehousing is the robotic
sorting system (RSS), distinguished by its characteristics such as
cost-effectiveness, simplicity, scalability, and adaptable throughput control.
While previous research has focused on analyzing the efficiency of RSS, it
often assumed an ideal robot management system ignoring potential queuing
delays by assuming constant travel times. This study relaxes this assumption
and explores the quantitative relationship between RSS configuration parameters
and system throughput. We introduce a novel robot traffic management method,
named the rhythmic control for sorting scenario (RC-S), for RSS operations,
equipped with an estimation formula establishing the relationship between
system performance and configurations. Simulations validate that RC-S reduces
average service time by 10.3\% compared to the classical cooperative A*
algorithm, while also improving throughput and runtime. Based on the
performance analysis of RC-S, we further develop a layout optimization model
for RSS, considering RSS configuration, desired throughput, and costs, to
minimize expenses and determine the best layout. Numerical studies show that at
lower throughput levels, facility costs dominate, while at higher throughput
levels, labor costs prevail. Additionally, due to traffic efficiency
limitations, RSS is well-suited for small-scale operations like
end-of-supply-chain distribution centers.
