Markov automata combine probabilistic branching, exponentially distributed delays and nondeterminism. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and stochastic scheduling. Their verification so far focused on single objectives such as (timed) reachability, and expected costs. In practice, often the objectives are mutually dependent and the aim is to reveal trade-offs. We present algorithms to analyze several objectives simultaneously and approximate Pareto curves. This includes, e.g., several (timed) reachability objectives, or various expected cost objectives. We also consider combinations thereof, such as on-time-within-budget objectives—which policies guarantee reaching a goal state within a deadline with at least probability p while keeping the allowed average costs below a threshold? We adopt existing approaches for classical Markov decision processes. The main challenge is to treat policies exploiting state residence times, even for untimed objectives. Experimental results show the feasibility and scalability of our approach.

马尔可夫自动机结合了概率分支，指数分布的延迟和不确定性。连续时间Markov决策过程的这种组成变量用于可靠性工程，性能评估和随机调度中。到目前为止，他们的验证仅集中在单个目标上，例如（定时）可达性和预期成本。在实践中，目标常常是相互依赖的，目的是揭示折衷方案。我们提出了可以同时分析多个目标并近似帕累托曲线的算法。例如，这包括几个（定时的）可达性目标或各种预期的成本目标。我们还考虑了它们的组合，例如预算内的按时目标，这些策略保证在期限内以至少概率p达到目标状态。同时将允许的平均费用保持在阈值以下？我们采用经典马尔可夫决策过程的现有方法。主要的挑战是开发状态停留时间的治疗策略，甚至取消定时目标。实验结果表明了该方法的可行性和可扩展性。