Analysis and Performance Evaluation of Markovian Feedback Multi-Server Queueing Model with Vacation and Impatience

Abstract

This paper deals with a finite capacity multi-server Markovian queueing model with Bernoulli feedback, synchronous multiple vacation policy and customers’ impatience (balking and reneging). By employing certain customer retention mechanism, impatient customers can be retained in the system. Applications of the suggested queueing model can be found in a wide variety of practical systems including modern information and communication technology (ICT) networks, call centers, and manufacturing systems. Using the recursive method, the steady state probabilities of the model are obtained. Various performance measures are derived. Then, some important particular cases are provided. Finally, different numerical examples are presented to demonstrate how the different parameters of the model influence the behavior of the stationary characteristics of the system.