M^X=M=c Queue with catastrophes and state-dependent control at idle time

Abstract

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

Key words： Markovian bulk-arriving queues; equilibrium distribution; queue size; recurrence; effective catastrophe

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