The analysis of behavioral models is of high importance for cyber-physical systems, as the systems often encompass complex behavior based on e.g. concurrent components with mutual exclusion or probabilistic failures on demand. The rule-based formalism of Probabilistic Timed Graph Transformation Systems (PTGTSs) is a suitable choice when the models representing states of the system can be understood as graphs and timed and probabilistic behavior is important. However, model checking PTGTSs is limited to systems with rather small state spaces.

We present an approach for the analysis of large-scale systems modeled as PTGTSs by systematically decomposing their state spaces into manageable fragments. To obtain qualitative and quantitative analysis results for a large-scale system, we verify that results obtained for its fragments serve as overapproximations for the corresponding results of the large-scale system. Hence, our approach allows for the detection of violations of qualitative and quantitative safety properties for the large-scale system under analysis. We consider a running example in which shuttles drive on tracks of a large-scale topology and autonomously coordinate their local behavior with other shuttles nearby. For this running example, we verify that (a) shuttles can always make the expected forward progress using several properties, (b) shuttles never collide, and (c) shuttles are unlikely to execute emergency brakes in two scenarios. In our evaluation, we apply an implementation of our approach in the tool AutoGraph to our running example.

行为模型的分析对于网络物理系统非常重要，因为系统通常包含基于例如具有互斥或按需概率故障的并发组件的复杂行为。当表示系统状态的模型可以理解为图形并且定时和概率行为很重要时，概率时序图转换系统 (PTGTS) 的基于规则的形式主义是一个合适的选择。然而，模型检查 PTGTS 仅限于状态空间相当小的系统。

我们通过系统地将状态空间分解为可管理的片段，提出了一种分析建模为 PTGTS 的大型系统的方法。为了获得大型系统的定性和定量分析结果，我们验证了为其片段获得的结果可以作为大型系统相应结果的过度近似。因此，我们的方法允许检测对所分析的大型系统的定性和定量安全属性的违反。我们考虑一个运行示例，其中航天飞机在大规模拓扑的轨道上行驶，并自主协调其与附近其他航天飞机的本地行为。对于这个正在运行的示例，我们验证了 (a) 航天飞机始终可以使用多个属性进行预期的前进，(b) 航天飞机永远不会发生碰撞，(c) 班车不太可能在两种情况下执行紧急制动。在我们的评估中，我们在工具中应用了我们的方法的实现 AutoGraph 到我们的运行示例。