Single Server Markovian Queuing System with Differentiated Working Vacations, Feedback and Impatience Customers

This study investigates a single server markovian queuing system with differentiated working vacations, feedback and impatience customers. Arrival is based on Poisson processes and the period of service is distributed exponentially. FCFS was used to serve the customer. There are two different kinds of vacations: the first kind begins after a busy duration, and the second kind starts when there are no customers waiting for the server to get back from vacation. The two vacations are exponentially distributed and independent. During the first kind and the second kind of vacations, services are exponentially distributed. Additionally, the impatience of the waiting consumer during the vacation period is taken into consideration. Customers who get successful service quit the system, but those who are dissatisfied return to the queue in the expectation of receiving successful service until they are delighted with their feedback. Consider the Stochastic Processes $\{(S(t), N(t)): t \geq 0\}$ This has been solved using the Matrix Geometric Method. Performance metrics are calculated using specific parameters. Furthermore, certain numerical and graphical tables are obtained.