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：非马尔可夫模型具有强大的表达能力，但其随机过程的分析较为复杂。随机状态类方法可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限制。仿真是另一种能够处理可通过逆变换采样的大类概率密度函数的方法，但其受困于罕见事件问题。我们结合这两种方法来分析非马尔可夫模型的时限瞬态特性。通过枚举状态空间树根节点附近的随机状态类，再借助仿真达到目标状态，从而实现对随机状态类方法不可行模型的瞬态评估，同时相较于单纯仿真降低了计算时间与瞬态概率估计量的方差。在罕见事件概率估计中观察到了具有前景的结果。