We present an efficient parametric model checking technique for the analysis of softwareperformability, i.e., of the performance and dependability properties of software systems. The new parametric model checking (pMC) technique works by using a heuristic to automatically decompose a parametric discrete-time Markov chain (pDTMC) model of the software system under verification into fragments that can be analysed independently, yielding results that are then combined to establish the required software performability properties. Our fast parametric model checking (fPMC) technique enables the formal analysis of software systems modelled by pDTMCs that are too complex to be handled by existing pMC methods. Furthermore, for many pDTMCs that state-of-the-art parametric model checkers can analyse, fPMC produces solutions (i.e., algebraic formulae) that are simpler and much faster to evaluate. We show experimentally that adding fPMC to the existing repertoire of pMC methods improves the efficiency of parametric model checking significantly, and extends its applicability to software systems with more complex behaviour than currently possible.

Parametric model checking (PMC) computes algebraic formulae that express key non-functional properties of a system (reliability, performance, etc.) as rational functions of the system and environment parameters. In software engineering, PMC formulae can be used during design, e.g., to analyse the sensitivity of different system architectures to parametric variability, or to find optimal system configurations. They can also be used at runtime, e.g., to check if non-functional requirements are still satisfied after environmental changes, or to select new configurations after such changes. However, current PMC techniques do not scale well to systems with complex behaviour and more than a few parameters. Our paper introduces a fast PMC (fPMC) approach that overcomes this limitation, extending the applicability of PMC to a broader class of systems than previously possible. To this end, fPMC partitions the Markov models that PMC operates with into fragments whose reachability properties are analysed independently, and obtains PMC reachability formulae by combining the results of these fragment analyses. To demonstrate the effectiveness of fPMC, we show how our fPMC tool can analyse three systems (taken from the research literature, and belonging to different application domains) with which current PMC techniques and tools struggle.

We present a new approach for synthesising Paretooptimal Markov decision process (MDP) policies that satisfy complex combinations of quality-of-service (QoS) software requirements. These policies correspond to optimal designs or configurations of software systems, and are obtained by translating MDP models of these systems into parametric Markov chains, and using multi-objective genetic algorithms to synthesise Pareto-optimal parameter values that define the required MDP policies. We use case studies from the service-based systems and robotic control software domains to show that our MDP policy synthesis approach can handle a wide range of QoS requirement combinations unsupported by current probabilistic model checkers. Moreover, for requirement combinations supported by these model checkers, our approach generates better Pareto-optimal policy sets according to established quality metrics.