Exploring non-Markovian dynamics: Stochastic analysis of a single-server retrial queue with recurrent clients and balking behavior under extended Bernoulli vacations.

The present study delves into the dynamics of a specific form of queueing system described as an retrial queue. Here, the queue comprises two distinct categories of clients: transit clients and recurrent clients. Transit clients are those who appear at the queue following a Poisson process, reflecting a random arrival pattern commonly seen in queueing scenarios.