Analysis of a Markovian retrial queueing system with impatience and vacation model

In the present study, we discuss about a single server retrial queueing structure along with impatience customers and vacation model. Especially, arrival of customers follows Poisson process. Exponential distribution of this model enhances the service time and retrial times. In the course of busy period, the customer may leave the system without entering the system. Otherwise the customers may join in the waiting room called orbit, in order to retry for their service. It is based on whether the customer will wait in the orbit till the service is rendered or exit the orbit before experiencing the service. Meanwhile when the system finds to be vacant then the server turns inactive and commences vacation. We established the queue size of the steady state equation of birth and death process by recursive approach. The performance measures are identified under the busy state, idle and vacation in order to examine the system and to demonstrate the characteristic of the queueing system.