Survivability of the MAP/PH/N queue with propagated failures

We consider the MAP/PH/N queueing system with propagated breakdowns. Breakdowns arrive in bunches (we call them attacks) according to the MAP. The process of further arrival of different types of server failures within an attack is governed by phase type Markov process. Recovering of the server takes an exponentially distributed time with intensity depending on the type of the occurred failure. We describe behavior of the system by the multi-dimensional continuous time Markov chain and analyze survivability of the system.