Markovian model of two heterogeneous server retrial queueing system with vacation and discouragement

The proposed model deals with the study of two server retrial queueing system with vacation times and discouraged customers. The servers under consideration are functioning with variant speeds to provide service. The customers will directly enter into the service channel if any one of the server is found free upon arrival. Otherwise, the customer will move to the orbit to occupy the server later. At the service completion epoch, the server turns to vacation state if no more customers were found in the waiting area. During this vacation or working period, the customers may leave the system forever due to their longer waiting time. This Markov model of birth-death process is developed using the Chapman-Kolmogorov governing equations. By using the recursive approach, we obtain the stationary distributions for the arriving customers. Few performance indices were identified to depict the behavior of the formulated model.