This paper considers replacement and maintenance policies for an operating unit which works at random times for jobs. The unit undergoes minimal repairs at failures and is replaced at a planned time T or at a number N of working times, whichever occurs first. The expected cost rate is obtained, and an optimal policy which minimizes it is derived analytically. The imperfect preventive maintenance (PM) model, where the unit is improved by PM after the completion of each working time, is analyzed. Furthermore, when the work of a job incurs some damage to the unit, the replacement model with number N is proposed. The expected cost rate is obtained by using theory of cumulative processes. Two modified models, where the unit is replaced at number N or at the first completion of the working time over time T, and it is replaced at T or number N, whichever occurs last, are also proposed. Finally, when the unit is replaced at time T, number N or Kth failure, whichever occurs first, the expected cost rate is also obtained.

It is an important problem to determine major collection times to meet the pause time goal for a generational garbage collector. From such a viewpoint, this paper proposes two stochastic models based on working schemes of a generational garbage collector: Garbage collections occur in a nonhomogeneous Poisson process, tenuring collection is made at a threshold level K, and major collection is made at time T or at Nth collection including minor and tenuring collections for the first model and at time T or at Nth collection including tenuring collections for the second model. Using the techniques of cumulative processes and reliability theory, expected cost rates are obtained, and optimal policies of major collection times which minimize them are discussed analytically and computed numerically.