(untitled) (Contemporary Mathematics, 2024)
In this paper, we can study about Markovian single-server queue with servers in distinct phases of disaster and repair. The server can stay in full-active Phase or passive Phase randomly and alternately. The server is set to serve in two Phases, such as the full active Phase and passive Phase. When the server operates in full active Phase, the customers arrive and served in First Come: First Serve (FCFS) queue discipline. However, when the server switches from full active to passive Phase, it can only offer to provide service at a rate lower than that of the server in full active Phase. During passive Phase, customers are not allowed to join the system. The server moves to repair Phase immediately after the last customer is served, irrespective of the Phase. The customers will be restricted from joining the queue in repair Phase. After the repair Phase, the server will enter the full active Phase. The server remains in the system for a random period of time. In the event of a disaster, in full active and passive Phases, all customers in system aredropped out, and system moves to repair Phase. The expressions for the steady state probabilities and some key performance metrics are obtained. A numerical illustration is made to study the effects of server shifting from full active phase to passive phase that affects the customers in the system and the occurrence of disaster which has an adverse effect on the customers in that phase.