Analysis of non-Markovian batch arrival retrial queue with priority services, vacation and vacation interruption under random environment, negative arrival, immediate feedback, differentiate breakdown, and repair

In this study, we construct a single server retrial queueing system with two classes of customers, vacation and vacation interruption under random environment, negative arrival, immediate feedback, differentiate breakdown and repair. Customers can be divided into two distinct categories, such as priority and ordinary. This concept emphasises non-preemptive priority discipline. Customers arrive according to Poisson processes for priority and ordinary. Both priority and regular customers can always receive the same service from the server, which is distributed arbitrarily. In this study, the time-dependent probabilities of system states using Laplace transforms are computed using the probability generating function and the supplementary variable technique. Numerical results are obtained which are also examined to facilitate the sensitivity analysis of system descriptions.