Analysis of MAP/PHF/c retrial queueing model with delayed feedback and non-persistence

This study focuses on a multi-server retrial queueing model with an infinite orbit capacity that examines customer behaviors, including balking, lack of persistence, and delayed feedback. Customers approach the system following a Markovian arrival process. We consider the possibility that failure may occur during customer service. If a failure occurs, the customer may either leave and retry later, restart the service from the beginning immediately, or continue from the point of failure. Importantly, the server remains operational after a failure. We utilize the phase-type with failures distribution to model this service time. The system’s behavior is represented as a multi-mensional continuous-time Markov chain whose infinitesimal generator is a level-dependent quasibirth and-death process. We demonstrate that this Markov chain falls within the category of asymptotically quasi-Toeplitz Markov chains to determine the ergodicity conditions. Further, we calculate steady-state probabilities and system efficiency metrics for this system. We also present numerical experiments that highlight how different parameters affect system performance.