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

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