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Queues with system disasters and impatient customers when system is down. (English) Zbl 1124.60076
Summary: Consider a system operating as an M/M/$$c$$ queue, where $$c =1$$, $$1< c <\infty$$, or $$c =\infty$$. 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.

##### MSC:
 60K25 Queueing theory (aspects of probability theory) 60K37 Processes in random environments 90B22 Queues and service in operations research
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