Achieving optimal resources utilisation in industrial environments: combining polling methods and an exhaustive service discipline with an unreliable service

Two types of queues, type I queue with infinite capacity and type II queue with a finite capacity, are both taken into account. While the service time distribution adheres to phase type, each queue's input process operates in line with the Markov arrival process (MAP). The server cycles through the line, starting with the type I queue, and provides standard service to everyone while also offering optional service based on the demands of the client. During the visiting period of each queue, a strict service discipline is observed. Working breakdown and repair are distributed exponentially, whereas many vacations are distributed according to a phase type. The entire number of consumers in the system are investigated using matrix analysis under the steady state probability vector. We analyse busy period analysis, an invariant probability vector, and few performance indicators in our model. The proposed model's numerical and graphical findings are also examined.