Continuously running software systems suffer from performance degradation due to aging phenomena and resource exhaustion that are mainly due to error conditions accumulation or due to exhaustion of system resources such as the physical memory. To counteract such phenomena, a periodic preemptive rollback to prevent software failures in the future, called software rejuvenation, can be applied. During the past 20 years, software rejuvenation has been extensively studied with the aim to design rejuvenation policies that optimize system availability, reliability, and performance, mainly in terms of operational cost. In this paper, we propose to model software systems’ overall performance capacity by assigning a performance capacity level at each of the possible states that it can be in, using a continuous time Markov process. A performance capacity indicator for all possible rejuvenation models incorporating partial, full, or both rejuvenation actions is defined and evaluated in the transient, and the steady state phase and the impact of various rejuvenation policies on it are further examined. Our aim is to distinguish the optimal, in terms of performance, rejuvenation strategy consisting of the type of rejuvenation to be implemented and the rejuvenation interval as well. Multi-objective optimization problems are additionally formulated for deriving the rejuvenation policies that optimize the system’s overall performance capacity with respect to availability and operational cost constraints. Numerical examples, in which through comparisons among the rejuvenation models and policies we can distinguish the optimal rejuvenation strategy to be followed, are also presented.

中文翻译：

---

具有多个退化级别的软件复兴模型的性能

持续运行的软件系统会因老化现象和资源耗尽而遭受性能下降，这主要是由于错误条件累积或由于物理内存等系统资源耗尽。为了抵消这种现象，可以应用周期性的抢先回滚以防止将来出现软件故障，称为软件恢复。在过去的 20 年中，软件更新得到了广泛的研究，旨在设计优化系统可用性、可靠性和性能的更新策略，主要是在运营成本方面。在本文中，我们建议通过使用连续时间马尔可夫过程在每个可能的状态分配性能容量级别来对软件系统的整体性能容量进行建模。在瞬态中定义和评估包含部分、完全或两者复兴动作的所有可能的复兴模型的性能容量指标，并进一步检查稳态阶段和各种复兴策略对其的影响。我们的目标是在性能方面区分最佳的返老还童策略，包括要实施的返老还童类型和返老还童间隔。此外，还制定了多目标优化问题，以推导出在可用性和运营成本约束方面优化系统整体性能能力的复兴策略。数值例子，其中通过比较回春模型和策略，我们可以区分要遵循的最佳回春策略，