Trade-off analysis meets probabilistic model checking

Probabilistic model checking (PMC) is a well-established and powerful method for the automated quantitative analysis of parallel distributed systems. Classical PMC-approaches focus on computing probabilities and expectations in Markovian models annotated with numerical values for costs and utility, such as energy and performance. Usually, the utility gained and the costs invested are dependent and a trade-off analysis is of utter interest. In this paper, we provide an overview on various kinds of non-standard multi-objective formalisms that enable to specify and reason about the trade-off between costs and utility. In particular, we present the concepts of quantiles, conditional probabilities and expectations as well as objectives on the ratio between accumulated costs and utility. Such multi-objective properties have drawn very few attention in the context of PMC and hence, there is hardly any tool support in state-of-the-art model checkers. Furthermore, we broaden our results towards combined quantile queries, computing conditional probabilities those conditions are expressed as formulas in probabilistic computation tree logic, and the computation of ratios which can be expected on the long-run.