A catastrophic queueing model with delayed action

A queueing model with catastrophes and delayed action is studied in this paper. This delayed action could be in the form of protecting or removing all the customers that are in the system based on the outcome of two random clocks which are simultaneously activated upon the occurrence of a catastrophic event. Assuming the customers to arrive according to a versatile Markovian point process to a single server system, the service times to be of phase type, and all other underlying random variables to be exponentially distributed, we use matrix-analytic methods to study the delayed catastrophic model in steady-state. Needed expressions for the number in the system as well as the waiting time distributions are derived along with a discussion on some special cases of this model. Detailed illustrative examples are presented