Reliability Analysis of a Batch Arrival Poisson Input Queue with Two Kinds of Heterogeneous Service and a General Start-Up Time Under \(N-policy\)

This article considers a single server vacation queueing model that requires some additional time to start a busy period (start-up time) under N-policy subject to unpredictable server breakdown. A single server provides two different services to its customers arriving in batches where the customers can facilitate optional repeated service once if desired. The server is allowed to take a single vacation after each busy period following a Bernoulli trial. The start-up, service, repeated service, and vacation times are generally distributed. For this model, the system reliability function (RF) in terms of Laplace Stieltjes Transform (LST) and mean time to first failure (MTTFF) of the server are analyzed analytically. Finally, the underlying model has been discussed in the context of functional analysis.