A multi-queue single-server model for storage and retrieval requests in a tier-captive AVS/RS

Autonomous vehicle storage and retrieval systems (AVS/RSs) have become increasingly popular owing to their high storage density and throughput. Previous research had primarily focused on system performances with different layout configurations; the role of input and output buffers (bays) in the system tiers were largely overlooked. Vehicle-blocking events can occur when the bays are full, causing delays and degrading the performance. In this study, we propose a model that differentiates storage requests (which wait physically in the input bay) from retrieval requests (which remain in storage locations as in an ’electronic’ queue). The aim of this study is to monitor the number of S-requests waiting in the input bay of the tier and the probability of vehicle-blocking events. This provides a valuable decision-support system for bay sizing in the warehouse pre design phase. Practical benefits include reduced number of blocking events, improved vehicle throughput, and guidance on recommended bay capacities. Although the proposed queueing model utilizes balance equations associated with a continuous-time Markov chain, we show that the performance results we seek are insensitive to the service-time distribution. A real-world case study provides insights into AVS/RS behaviour under various arrival rates and different dispatching policies.