On a characteristic of a single-server system with an unreliable device. (English. Russian original) Zbl 0632.60096

Prizva, G. I.

Theory Probab. Math. Stat. 35, 97-101 (1987); translation from Teor. Veroyatn. Mat. Stat. 35, 87-91 (1986).

A queue M/G/1/\(\infty\) is under consideration. It is supposed that the server can break down only when being free. Namely if the server became free at time t then it will break down up to time \(t+x\) with probability \(D_ 0(x)\). Let \(\theta\) (t) and \(\omega\) (t) be the lengths of time intervals both beginning from the moment t, \(\theta\) (t) ending at the nearest moment after t when the system is free of customers and the server is in working state; \(\omega\) (t) ending at the first moment after t when the system is free of the customers which entered before the time t and the server is in working state. The joint distribution of \(\omega\) (t) and \(\theta\) (t) and the limit (t\(\to \infty)\) distribution in terms of Laplace-Stieltjes transform are obtained.

Reviewer: V.V.Kalashnikov

MSC:

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

Keywords:

single-server queue; waiting time; busy period; Laplace-Stieltjes transform