Gaver's parallel system attended by a cold standby unit and a repairman with multiple vacations

This paper studies the Gaver's parallel repairable system attended by a cold standby unit and a repairman with multiple vacations. It is assumed that the operating time of units has an exponential distribution, while the repair time and the vacation time have general continuous distributions. Using vector Markov process theory and Laplace transform method, we obtain the Laplace transform of the reliability, the mean time to first failure, the steady-state availability and the steady-state failure frequency and so on. In addition, we also investigate the parameters' effect on the steady-state availability by numerical comparison and analyze the benefit of the system.