Non-Markovian models have great expressive power, at the cost of complex analysis of the stochastic process. The method of Stochastic State Classes (SSCs) derives closed-form analytical expressions for the joint Probability Density Functions (PDFs) of the active timers with marginal expolynomial PDF, though being hindered by the number of concurrent non-exponential timers and of discrete events between regenerations. Simulation is an alternative capable of handling the large class of PDFs samplable via inverse transform, which however suffers from rare events. We combine these approaches to analyze time-bounded transient properties of non-Markovian models. We enumerate SSCs near the root of the state-space tree and then rely on simulation to reach the target, affording transient evaluation of models for which the method of SSCs is not viable while reducing computational time and variance of the estimator of transient probabilities with respect to simulation. Promising results are observed in the estimation of rare event probabilities.

翻译：非马尔可夫模型虽具备强大的表达能力，但其随机过程的分析往往十分复杂。随机状态类方法能够为具有边缘指数多项式概率密度函数的活跃计时器推导出联合概率密度函数的闭式解析表达式，但该方法受到并发非指数计时器数量以及再生间离散事件数量的制约。仿真作为替代方案能够处理可通过逆变换采样的大类概率密度函数，但其面临稀有事件问题。本研究融合这两种方法以分析非马尔可夫模型的时界瞬态特性。通过在状态空间树根部附近枚举随机状态类，继而借助仿真抵达目标状态，实现了对随机状态类方法无法处理的模型进行瞬态评估，同时相较于纯仿真方法降低了计算时间与瞬态概率估计量的方差。在稀有事件概率估计中观察到了具有前景的结果。