Queues with system disasters and impatient customers when system is down

Consider a system operating as an M/M/c queue, where c=1, 1<c<∞, or c=∞. The system as a whole suffers occasionally a disastrous breakdown, upon which all present customers (waiting and served) are cleared from the system and lost. A repair process then starts immediately. When the system is down, inoperative, and undergoing a repair process, new arrivals become impatient: each individual customer, upon arrival, activates a random-duration timer. If the timer expires before the system is repaired, the customer abandons the queue never to return. We analyze this model and derive various quality of service measures: mean sojourn time of a served customer; proportion of customers served; rate of lost customers due to disasters; and rate of abandonments due to impatience.