This paper proposes a novel abstraction technique for continuous-time Markov chains (CTMCs). Our technique fits within the realm of three-valued abstraction methods that have been used successfully for traditional model checking. The key idea is to apply abstraction on uniform CTMCs that are readily obtained from general CTMCs, and to abstract transition probabilities by intervals. It is shown that this provides a conservative abstraction for both true and false for a threevalued semantics of the branching-time logic CSL (Continuous Stochastic Logic). Experiments on an infinite-state CTMC indicate the feasibility of our abstraction technique.

A continuous-time Markov decision process (CTMDP) is a generalization of a continuous-time Markov chain in which both probabilistic and nondeterministic choices co-exist. This paper presents an efficient algorithm to compute the maximum (or minimum) probability to reach a set of goal states within a given time bound in a uniform CT-MDP, i.e., a CTMDP in which the delay time distribution per state visit is the same for all states. We prove that these probabilities coincide for (time-abstract) history-dependent and Markovian schedulers that resolve nondeterminism either deterministically or in a randomized way.

We introduce a framework to study stochastic systems, i.e. systems in which the time of occurrence of activities is a general random variable. We introduce and discuss in depth a stochastic process algebra (named Q) adequate to specify and analyse those systems. In order to give semantics to Q, we also introduce a model that is an extension of traditional automata with clocks which are basically random variables: the stochastic automata model. We show that this model and Q are equally expressive. Although stochastic automata are adequate to analyse systems since they are finite objects, they are still too ·coarse to serve as concrete semantic objects. Therefore, we introduce a type of probabilistic transition system that can deal with arbitrary probability spaces.In addition, we give a finite axiomatisation for Q that is sound for the several semantic notions we deal with, and complete for the finest of them. Moreover, an expansion law is straightforwardly derived.

RAMS (Reliability, Availability, Maintenance, Safety) requirements are utmost important for safety-critical systems like railroad infrastructure and signaling systems, and often imposed by law or other government regulations. Fault tree analysis (FTA, for short) is a widely applied industry standard for RAMS analysis [1,2], and is often one of the techniques preferred by railways organizations [3]. FTA yields system availability and reliability, and can be used for critical path analysis. It can however not yet deal with a pressing aspect of railroad engineering: maintenance. While railroad infrastructure providers are focusing more and more on managing cost/performance ratios, RAMS can be considered as the performance specification, and maintenance the main cost driver. Methods facilitating the management of this ratio are still very uncommon. This paper presents a powerful, flexible and transparent technique to incorporate a maintenance aspects in fault tree analysis, based on stochastic model checking. We are able to analyze and compare different maintenance strategies (such as age-based, clock-based and condition-dependent maintenance) and their impact on reliability and availability metrics. Thus, we facilitate the trade off between cost and RAMS performance.To keep the underlying state space of our state space small, we deploy two aggressive state space reduction techniques, namely compositional aggregation, and smart semantics. We illustrate our approach on several existing, large fault tree models in a case study from Movares, a major RAMS consultancy firm in the Netherlands.

This paper presents a process algebra for specifying soft real-time constraints in a compositional way. For these soft constraints we take a stochastic point of view and allow arbitrary probability distributions to express delays of activities. The semantics of this process algebra is given in terms of stochastic automata, a variant of timed automata where clocks are initialised randomly and run backwards. To analyse quantitative properties, an algorithm is presented for the on-the-fly generation of a discrete-event simulation model from a process algebra specification. On the qualitative side, a symbolic technique for classical reachability analysis of stochastic automata is presented. As a result a unifying framework for the specification and analysis of quantitative and qualitative properties is obtained. We discuss an implementation of both analytic methods and specify and analyse a fault-tolerant multi-processor system.