Abstract. This paper describes a major new release of the PRISM probabilistic model checker, adding, in particular, quantitative verification of (priced) probabilistic timed automata. These model systems exhibiting probabilistic, nondeterministic and real-time characteristics. In many application domains, all three aspects are essential; this includes, for example, embedded controllers in automotive or avionic systems, wireless communication protocols such as Bluetooth or Zigbee, and randomised security protocols. PRISM, which is open-source, also contains several new components that are of independent use. These include: an extensible toolkit for building, verifying and refining abstractions of probabilistic models; an explicit-state probabilistic model checking library; a discrete-event simulation engine for statistical model checking; support for generation of optimal adversaries/strategies; and a benchmark suite. 1

We introduce Fortuna, the first tool for model checking priced probabilistic timed automata (PPTAs). Fortuna can handle the combination of real-time, probabilistic and cost features. This is required for addressing key design trade-offs that arise in many practical applications such as the Zeroconf, Bluetooth, IEEE802.11 and Firewire protocols, protocols for sensor networks, and scheduling problems with failures. PPTAs are an extension of probabilistic timed automata (PTAs) with cost-rates and discrete cost increments on states. Fortuna is able to compute the maximal probability by which a state can be reached under a certain cost-bound (and time-bound). Although this problem is undecidable in general, there exists a semi-algorithm that produces a non-decreasing sequence of probabilities converging to the maximum. This paper presents a number of crucial optimizations of that algorithm. We compare the performance of Fortuna with existing approaches for PTAs. Surprisingly, although PPTAs are more general, our techniques exhibit superior performance.

Abstract. This tutorial provides an introduction to probabilistic model checking, a technique for automatically verifying quantitative properties of probabilistic systems. We focus on Markov decision processes (MDPs), which model both stochastic and nondeterministic behaviour. We describe methods to analyse a wide range of their properties, including specifications in the temporal logics PCTL and LTL, probabilistic safety properties and cost- or reward-based measures. We also discuss multiobjective probabilistic model checking, used to analyse trade-offs between several different quantitative properties. Applications of the techniques in this tutorial include performance and dependability analysis of networked systems, communication protocols and randomised distributed algorithms. Since such systems often comprise several components operating in parallel, we also cover techniques for compositional modelling and verification of multi-component probabilistic systems. Finally, we describe three large case studies which illustrate practical applications of the various methods discussed in the tutorial. 1