Abstract. We propose a conceptually simple technique for verifying probabilistic models whose transition probabilities are parametric. The key is to replace parametric transitions by nondeterministic choices of extremal values. Analysing the resulting parameter-free model using off-theshelf means yields (refinable) lower and upper bounds on probabilities of regions in the parameter space. The technique outperforms the existing analysis of parametric Markov chains by several orders of magnitude regarding both run-time and scalability. Its beauty is its applicability to various probabilistic models. It in particular provides the first sound and feasible method for performing parameter synthesis of Markov decision processes.

We present the probabilistic model checker Storm. Storm supports the analysis of discrete- and continuous-time variants of both Markov chains and Markov decision processes. Storm has three major distinguishing features. It supports multiple input languages for Markov models, including the Jani and Prism modeling languages, dynamic fault trees, generalized stochastic Petri nets, and the probabilistic guarded command language. It has a modular setup in which solvers and symbolic engines can easily be exchanged. Its Python API allows for rapid prototyping by encapsulating Storm’s fast and scalable algorithms. This paper reports on the main features of Storm and explains how to effectively use them. A description is provided of the main distinguishing functionalities of Storm. Finally, an empirical evaluation of different configurations of Storm on the QComp 2019 benchmark set is presented.

Abstract. Computing reachability probabilities is at the heart of probabilistic model checking. All model checkers compute these probabilities in an iterative fashion using value iteration. This technique approximates a fixed point from below by determining reachability probabilities for an increasing number of steps. To avoid results that are significantly off, variants have recently been proposed that converge from both below and above. These procedures require starting values for both sides. We present an alternative that does not require the a priori computation of starting vectors and that converges faster on many benchmarks. The crux of our technique is to give tight and safe bounds-whose computation is cheap-on the reachability probabilities. Lifting this technique to expected rewards is trivial for both Markov chains and MDPs. Experimental results on a large set of benchmarks show its scalability and efficiency.

Quantitative formal models capture probabilistic behaviour, real-time aspects, or general continuous dynamics. A number of tools support their automatic analysis with respect to dependability or performance properties. QComp 2019 is the first, friendly competition among such tools. It focuses on stochastic formalisms from Markov chains to probabilistic timed automata specified in the Jani model exchange format, and on probabilistic reachability, expected-reward, and steady-state properties. QComp draws its benchmarks from the new Quantitative Verification Benchmark Set. Participating tools, which include probabilistic model checkers and planners as well as simulation-based tools, are evaluated in terms of performance, versatility, and usability. In this paper, we report on the challenges in setting up a quantitative verification competition, present the results of QComp 2019, summarise the lessons learned, and provide an outlook on the features of the next edition of QComp.

We present an extensive collection of quantitative models to facilitate the development, comparison, and benchmarking of new verification algorithms and tools. All models have a formal semantics in terms of extensions of Markov chains, are provided in the Jani format, and are documented by a comprehensive set of metadata. The collection is highly diverse: it includes established probabilistic verification and planning benchmarks, industrial case studies, models of biological systems, dynamic fault trees, and Petri net examples, all originally specified in a variety of modelling languages. It archives detailed tool performance data for each model, enabling immediate comparisons between tools and among tool versions over time. The collection is easy to access via a client-side web application at qcomp.org with powerful search and visualisation features. It can be extended via a Git-based submission process, and is openly accessible according to the terms of the CC-BY license.

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Abstract. We provide an efficient algorithm for multi-objective modelchecking problems on Markov decision processes (MDPs) with multiple cost structures. The key problem at hand is to check whether there exists a scheduler for a given MDP such that all objectives over cost vectors are fulfilled. Reachability and expected cost objectives are covered and can be mixed. Empirical evaluation shows the algorithm's scalability. We discuss the need for output beyond Pareto curves and exploit the available information from the algorithm to support decision makers.

Abstract. Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. 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-timewithin-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.