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.

Software rejuvenation is a preventive and proactive solution that is particularly useful for counteracting the phenomenon of software aging. In this article, we consider periodic software rejuvenation models based on the expected cost per unit time in the steady state under discrete-time operation circumstance. By applying the discrete renewal reward processes, we describe the stochastic behavior of a telecommunication billing application with a degradation mode, and determine the optimal periodic software rejuvenation schedule minimizing the expected cost. Similar to the earlier work by the same authors, we develop a statistically non-parametric algorithm to estimate the optimal software rejuvenation schedule, by applying the discrete total time on test concept. Numerical examples are presented to estimate the optimal software rejuvenation schedules from the simulation data. We discuss the asymptotic behavior of estimators developed in this paper.