The generalized Mx/G(M/G)/1(M/G) repairable queueing system (II): Some reliability indices

In this paper we further study the generalized Mx/G(M/G)/1(M/G) repairable queueing system and discuss the following reliability problems of the service station: (1) The probability that it fails at time t; (2) The failure number during the server busy period; (3) The expected failure number and its asymptotic expansion during (0, t]; (4) The downtime during the server busy period; (5) The expected downtime and its asymptotic expansion during (0, t], and obtain a series of results, while simultaneously giving some asymptotic formulas for calculating the expected failure number and expected downtime during (0, t].