Some reliability problems arising in M/G/1 queueing system with repairable service station and server vacations

This paper consider an M/G/1 queueing system with repairable station and server vacations. Suppose that the life length of the up and operating service station has an exponential distribution and the repair time length of the broken service station and the vacation time length of the server have general distributions, then the following reliability problems of the service station are discussed: (a) The probability that it fails at time t, i.e. its unavailability; (b) The failure number during the `server busy period', (c) The expected failure number during (0, t] and its asymptotic expansion, (d) The downtime during the `server busy period'; (e) The expected downtime during (0, t] and its asymptotic expansion. Some reliability results of the service station are obtained. Simultaneously some asymptotic formulas for calculating the expected failure number and expected downtime during (0, t] are also given.