Fixed Batch Service Queueing Model Under Deterministic Arrivals with Multiple Vacations and Reset Mechanism

In this present work A single server fixed batch queuing method is considered with fixed arrival and service occurs according to poisson process, under multiple vacation and system reset. Further, It is supposed that the vacation has an exponential distribution and that the system reset happens as a Poisson process. In this model, the system starts with k customers, and the server immediately begins service for a batch of size k. When a service is finished and there are fewer than k customers in line, the server takes a vacation. When the vacation ends, If the count of customers is still insufficient, the server continues taking multiple vacations of average length 1/α. If there are k or more customers, the server selects the first k customers and starts the next batch service. The system also considers the possibility of a system reset. Whenever a reset occurs, all customers in the system are removed, and the server goes on a vacation. Numerical experiments and graphical representations are used to study the mean and variance change with different Different rates for service rate, batch size, vacation rate, and reset rate have been considered in the present study. It has been observed that the developed model is helpful in the analysis of the performance of automatic service systems facing periodic disruptions.