Markovian Queueing System in Retrial Queue with Optional Services and Feedback Behaviour

This study analyzes a markovian queueing system in retrial queue with optional services and feedback behaviour. Customer arrivals follow a Poisson distribution and service times follow an exponential distribution. When the server is unoccupied, the arriving customer is provided service without delay. The customer sees the server is busy, they may join the orbit or wait in the system. After an arbitrary period of time, the customer may retry their request for service from the orbit. After completing the First Essential Service (FES), which is mandatory primary service that is required, every customer has the option to either exit the system or pursue the Second Optional Service (SOS). The customer may exit the system after the service is satisfied, and the unsatisfied customer follows up as a feedback customer. Consider the Stochastic Processes$\{(L(t), M(t)): t \geq \mathbf{0}\}$, the probability vectors were derived by Matrix Geometric Method and Numerous metrics related to system performance are computed and the impact of the system parameters on the performance metrics is analysed both statistically and graphically.