A general bulk service queue with arrival rate dependent on server breakdowns

AbstractA single-server queueing system with general bulk service that alternates stochastically between operational state and failed (or repair) state is considered. The system, when operational, functions as a single-server Poisson queue with general bulk service. When it fails, no service occurs but customers continue to arrive according to a Poisson process; however, the arrival rate is different from that when the system is operational. The durations of the operating periods and repair periods follow exponential and phase-type distributions, respectively. The steady-state probability vector of the number of customers in the queue and the stability condition are obtained using a matrix-geometric algorithmic approach