A STUDY ON THREE-STAGE TANDEM QUEUEING SYSTEMS WITH POISSON INPUT AND LOAD-DEPENDENT SERVICE MECHANISMS

Queueing theory plays a crucial role in analyzing congestion and optimizing resource utilization in complex systems. Traditional models often assume stationary arrival and service processes, typically modeled using homogeneous Poisson processes. However, in many practical scenarios, such as hospital operations, manufacturing systems, cloud computing, and airport security, service rates are time-dependent and are more accurately captured by NHPP. This study presents a three-node tandem queueing model where each node features a time-dependent service mechanism governed by a NHPP. We derive key performance metrics, including the typical No. of Users in line, the duration Users spend before receiving service at each stage and across the entire system, the overall throughput, and the variation in the No. of Users present. A thorough sensitivity analysis is conducted to explore how different service rate parameters impact these PMs. The results highlight the significant effect of time-dependent service dynamics on system behavior, demonstrating that the proposed model offers a more accurate and flexible framework for studying systems with time-varying service processes. Additionally, this three-node model generalizes and extends earlier two-node configurations, providing deeper insights into multi-stage service environments