Modeling of Stochastic Priority BI-Tandem and Parallel Queue Network with Revisiting Facility

This paper presents a comprehensive mathematical analysis of a queueing network model having four servers, two of them are in bi-series and other two are in parallel arrangement, incorporating a single revisiting facility under a stochastic environment. The servers in the bi-series configuration are further connected in series with the parallel servers to forms a queue structure. Arrival and Service unit follow a Poisson distribution and the pre-emptive priority discipline is followed at the entry level for the first and second servers. A key feature of the model is the incorporation of a single customer revisiting facility, governed by different probabilistic feedback mechanisms at each server. By using Generating and partial function techniques, the solution of the differential differences equations in steady state condition has been calculated. The main objective of this paper is to evaluate the queue performance metrics of the queueing model like average queue length, server utilization, total time spent by the customers and variance in queues. A comparative analysis of the model with literature data has been done to show the validation of the model and demonstrating consistency and highlighting its enhanced flexibility in modeling real-life queueing environments. The impact of priority mechanism and revisit probabilities on system behavior is systematically explored through numerical illustrations. For better and deeper understanding of the model's behavior, graphical illustrations are provided to support and visualize the findings. The results provide valuable insights for optimizing service efficiency in complex networked systems, particularly in domains such as telecommunications and manufacturing systems.