Analysis of an unreliable single server batch arrival queue with two types of services under Bernoulli vacation policy

This article considers a single server batch arrival queue providing two types of general heterogeneous parallel services under Bernoulli Vacation Policy. The server assumed here is unreliable and incorporates the concept of delayed repair period. An extensive study of this model is carried out and the queue size distribution at random as well as departure epoch is obtained. Further, Laplace Stieltjes Transform of a busy period and waiting time distribution is also being derived. Finally, some important performance measures along with the reliability indices are accomplished in the study.