  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.
