Performance analysis of a queueing system with tandem nodes, retrial and server vacations

Abstract

In this proposed work, we consider a Markovian model of two-stage tandem queueing system with retrial policy and server vacation. The arriving customers are directed to the first station for service if server is idle upon arrival. Otherwise, they will enter into the orbit for retrial. These customers will generate a continuous stream of request for service in a random period of time. After completing the first station service, the customers will enter into the second station. Once the customers receive their service in both stations, they will depart from the system forever. It is mandatory for all the arriving customers to come across both the service stations. When no more customers are present in the orbit, the servers will leave for vacation. The balance equations of birth–death transitions are solved using the recursive approach. Various system performance measures are obtained and the effect of parameters were illustrated graphically.