Reliability Analysis of an Unreliable N-Policy Queue Under Bernoulli Vacation Schedule with Two-Service Genres and Optional Repeated Service

This research study undertakes a bulk arrival single server queue rendering two-heterogeneous services with optional re-service, under Bernoulli vacation schedule and [Formula: see text]-policy subject to a random breakdown of the service station. For this model, Laplace–Stieltjes transform of the system reliability function is obtained using the supplementary variable technique. Further, the performance measure mean time to first failure of the server is derived. Moreover, a detailed numerical investigation of the model is carried out to show the applicability of the model.