We employ uncertain parametric CTMCs with parametric transition rates and a prior on the parameter values. The prior encodes uncertainty about the actual transition rates, while the parameters allow dependencies between transition rates. Sampling the parameter values from the prior distribution then yields a standard CTMC, for which we may compute relevant reachability probabilities. We provide a principled solution, based on a technique called scenario-optimization, to the following problem: From a finite set of parameter samples and a user-specified confidence level, compute prediction regions on the reachability probabilities. The prediction regions should (with high probability) contain the reachability probabilities of a CTMC induced by any additional sample. To boost the scalability of the approach, we employ standard abstraction techniques and adapt our methodology to support approximate reachability probabilities. Experiments with various well-known benchmarks show the applicability of the approach.
翻译:我们使用具有参数过渡率和参数值之前的不确定参数CTMC。 先前的编码编码了实际过渡率的不确定性, 而参数允许过渡率之间的依赖性。 从先前的分布中抽样参数值,然后得出一个标准的CTMC, 我们可以计算出相关的可实现性概率。 我们根据一种称为假设-优化的技术, 向下列问题提供了原则性解决办法: 从一组有限的参数样本和用户指定的信任度, 计算出对可实现性概率的预测区域。 预测区域应该( 高概率) 包含由任何其他样本引致的CTMC的可实现性概率。 为了提高该方法的可扩展性, 我们采用标准的抽象技术, 并调整我们的方法, 以支持近似可实现概率。 各种已知基准的实验显示了该方法的适用性。