A state dependent arrival analysis in a non-Markovian bulk queue with server failures

Breakdown brings a huge impact in the queueing system, which causes complicated consequences. This paper comprises the results of functioning and malfunctioning of the queueing system due to continuous server breakdown. This work examines the failure of the server without interruption in state-dependent arrivals and numerous vacations. Even if a failure happens, the server is not stopped for maintenance before finishing a batch of service. The queue size PGF at an irrational time period, as well as the probability generating functions of vacation, service, and renovation completion epochs, are derived using the additional variable technique. The queueing system's unique qualities and key features are provided, along with a cost model. An extensive numerical research is done using real-world examples.