Poisson Input and Exponential Service Time Finite Population Interdependent Queueing Model Having Parallel Servers with Breakdown and Controllable Arrival Rates

Articles describing the limited capacity of malfunctioning and operating services exist, but this article aims to connect the rates of controllable arrivals and the interdependence of the arrival-and-service procedure. The study of parallel servers with breakdown and controlled arrival rates and the clients approach the system individually in a Poisson procedure. The arrival pattern follows a Poisson procedure, and service follows an exponential. In real-life situations, if we go to a toll plaza, there is a parallel server available for every client. The server furnishes the service individually, first-come, first-served (FCFS). At that time, if the machine breaks down, no service will occur until it is repaired, so the count of clients waiting in queue increases. These models are used to analyze practical situations such as import and export ships, taxi stands, computer-related applications for time-sharing, system architecture, and so on. Numerical examples are calculated using MATLAB software, and graphical analysis is provided for better comprehension. According to this article, this method has a finite population of parallel servers. Future study of the proposed model is included in this study.