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.

This study examines a single-server queue approach that discourages arrivals, accounts for impatient customers, and includes a self-switching server is considered. A queue with a single self-switching server, subjected to discouraged arrivals and customer impatience, is analyzed. Customers arrive at a rate of λ/(n+1), where λ denotes a positive constant and n corresponds to the total number of customers in the system. The server provides service at a rate of µ1 until the size of the system is smaller than K. Once the system size reaches K, the server switches to a faster service rate of µ2. After joining the queue, customers become impatient and abandon the system at a rate of ξ until the server switches to the fast service rate. There is no impatience once the server starts serving at the faster rate. The steady-state probability distribution of this system is determined, and its performance metrics, such as expected wait time and the number of customers likely to join the queue or system, are provided. Numerical illustrations are also included.

In this research, we have introduced compartments for asymptomatic and symptomatic individuals, along with reduced susceptibility, as key factors defining our investigation. The study is carried out in diverse scenarios, considering them as crucial for the essential generation number of the model, set at 3.18( r 0 > 1 ). The persistent reproduction differential method was used to explore the impact of continuous adrenocorticotropic hormone (ACTH) administration on the global gene expression in primary cultures of both fetal and adult adrenal cells. The study also investigates ACTH’s genetic effects on both adult and fetal human adrenal cells. The conclusion of this study is demonstrated through relevant and correct medical applications.