Limit behaviour of a controlled recovery system \(\vec M_{\mu}/M_{\mu}/n\). (Russian) Zbl 0697.90027

Strik, Ya.

Teor. Veroyatn. Mat. Stat., Kiev 41, 116-120 (1989).

The author studies machine interference problems in the case where the rates of failures and repairs depend on the state of some controlling Markov chain. Under the assumption of “fast” repair it is shown that the normalized time until the first failure has asymptotically exponential distribution and the scaled number of failure weekly converges to a Poisson process.

Reviewer: G.Falin

MSC:

90B22	Queues and service in operations research
60K25	Queueing theory (aspects of probability theory)
90B25	Reliability, availability, maintenance, inspection in operations research

Keywords:

fast repair; machine interference problems; failures; repairs; controlling Markov chain; asymptotically exponential distribution; Poisson process