An Analysis of Multi-Tiered Feedback Queueing Networks with Four Servers Motivated by Automated Logistics Systems

Abstract

In the Automated logistics systems highly efficient material handling is required to manage fluctuating flow capacity and complex routing demands. This queueing network applications with important multi-tiered feedback of logistics networks operating with four different servers, one central server linked with the three parallel servers, on a modern automated sorting facilities and distribution centre like amazon fulfilment centre. We model the system as a queueing network where items traverse within multiple parallel tiers after reaching the central server, incorporating feedback loops to simulate re-routing, sorting exceptions, and multi-server processing tasks. Furthermore, we investigate the impact of server allocation policies and routing probabilities on bottlenecks and total system delay. Numerical simulations validate the analytical model, demonstrating how optimal tier configuration and feedback management can significantly enhance operational efficiency. The results provides practical design guidelines for logistics engineers/managers aiming to minimize congestion and maximize throughput in automated Amazon fulfilment warehousing environments.