Analysis of Batch Encouraged Arrival Markovian Model Due to a Secondary Optional Service, Break-Down and Numerous Vacations

Abstract

In this study, we describe a batch encouraged arrival Markovian queuing model due to a secondary optional service, breakdown and numerous vacations. In this model, encouraged arrival is introduced, the server goes on vacation every time the system empties and the length of the vacation is predicted to follow an exponential distribution. If the server returns from vacation and there are no customers in line, he will take another vacation until there is at minimum one unit in the system. The steady-state findings have been derived and the time-dependent Probability- Generating- Functions (PGF) have been determined in terms of their Laplace transforms. In this model, we also discover the average queue length and average waiting time have been obtained.