MATHEMATICAL ANALYSIS OF FEEDBACK QUEUE NETWORK MODEL WITH PRIORITVY COMPRISED OF TWO SERIAL CHANNELS WITHIN STOCHASTIC CONDITIONS

Source abstract

This paper presents a comprehensive analysis of a feedback queue model with a Priority mechanism and investigates its behavior under stochastic conditions. This model comprises two serially connected service channels, with priority applied exclusively to the first service channel. Upon entry, customers are classified into two groups-low and high priority. A preemptive priority discipline is used at the first server to distinguish between high- and low-priority customers, thereby reflecting real-world service hierarchies. The feedback mechanism in the model allows for a maximum of one time only for the customer’s satisfaction with the service. The arrival of the customers is governed by a Poisson process and and service times at both servers are assumed to follow independently and be exponentially distributed. Upon service completion at the second server, customers may either exit the system permanently or re-enter the network through a feedback loop. The Steady-state behavior of the system is captured through a set of differential equations, which are solved by using the generating function technique combined with classical calculus laws. Various queue performance indicators, including average queue length, variance in queues, server utilization, and total duration time, are discussed. In the last section, a comparative study of the model with the literature is also discussed. The model’s behaviour is well demonstrated both graphically and numerically and provides an in-depth understanding of how each parameter influences the overall system performance, and the obtained results prove the stability and accuracy of the model. The insights derived from the analysis could help understand the design and optimization of the queueing model in different settings such as hospitals, manufacturing industries, and telecommunications.