The M^X/M/c queue with state-dependent control at idle time and catastrophes

IIn this paper, we consider an M^X/M/c queue with state-dependent control at idle time and catastrophes. Properties of the queues which terminate when the servers become idle are firstly studied. Recurrence, equilibrium distribution and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these results and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we can obtain the Laplace transform of the transition probability for the absorptive M^X/M/c queue.