Analytical Study of Heterogeneous Feedback Queue Model with Priority and Atmost One-Time Revisit Facility

This paper deals with a queuing model incorporates three service channels, the first channel being entry point is connected to two heterogeneous channels. The arrival process of the customers is modeled using Poisson distribution and the service rates of the customer follow exponential distribution. At the entry level, the system adopts a Preemptive priority discipline, which confirms that higher priority customers are served first. In addition, Feedback of the customers is allowed at each of the service channels enabling customers to revisit the service channels which are limited to a maximum of one. Notably, the probability of the customers for a second visit is different as the probability of the first visit, demonstrating additional level of complexity. The steady-state differential equations have been derived and apply the generating function techniques to solve them. The main purpose of this paper is to examine the behavior of the feedback queue model under a priority service discipline in a stochastic environment. The performance measures such as utilization factors of different servers, total waiting time, fluctuation in queues and average queue length are calculated, offering comprehensive analysis of the system’s efficiency. The model has been illustrated with the use of numerical examples to demonstrate the practical applicability of the model and also serves to validate the proposed model. The results are visually shown by graphical plots. It participates to a deeper understanding of feedback and priority mechanisms to show the impact of this mechanism on queue performance within stochastic environment, with practical applications in fields such as manufacturing, industries and telecommunications.