A study on the performance measures of the non-Markovian model of optional types of service with extended vacation, reneging process and service interruption followed by phases of repair

In this study on a non-Markovian queuing framework, clients arriving in batches follow a Poisson distribution. All the arriving clients have the alternative of picking any of the N sorts of services rendered. Service time follows general distribution. In addition, the system breaks down at random. Hence the server gets into repair process of two phases based on the fault, in first phase general repair is carried out. Then in the second phase repair based on the category is followed. Likewise after the system ends up with service, the server will go for a necessary vacation. In addition, an optional extended vacation is followed. In this vacation time, maintenance work is carried out. An additional aspect of reneging happens during the time of break down and vacation due to impatience of the customers. By the use of birth and death queuing process the conditions overseeing the model is framed. The probability generating queue size and queuing execution measures of the model are derived. The legitimisation of the model is finished by methods for numerical illustration. The graphical portrayal gives a reasonable picture about the procedure. Also, it gives significant thoughts for decrease the system break down, reneging and for the advance of the system speedier.