Smoothed model checking based on Gaussian process classification provides a powerful approach for statistical model checking of parametric continuous time Markov chain models. The method constructs a model for the functional dependence of satisfaction probability on the Markov chain parameters. This is done via Gaussian process inference methods from a limited number of observations for different parameter combinations. In this work we incorporate sparse variational methods and active learning into the smoothed model checking setting. We use these methods to improve the scalability of smoothed model checking. In particular, we see that active learning-based ideas for iteratively querying the simulation model for observations can be used to steer the model-checking to more informative areas of the parameter space and thus improve sample efficiency. We demonstrate that online extensions of sparse variational Gaussian process inference algorithms provide a scalable method for implementing active learning approaches for smoothed model checking.

In this paper we consider the problem of policy synthesis for systems of large numbers of simple interacting agents where dynamics of the system change through information spread via broadcast communication. By modifying the existing modelling language Carma and giving it a semantics in terms of continuous time Markov decision processes we introduce a natural way of formulating policy synthesis problems for such systems. However, solving policy synthesis problems is difficult since all non-trivial models result in very large state spaces. To combat this we propose an approach exploiting the results on fluid approximations of continuous time Markov chains to obtain estimates of optimal policies.

High availability is one of the core properties of Infrastructure as a Service (IaaS) and ensures that users have anytime access to on-demand cloud services. However, significant variations of workflow and the presence of super-tasks, mean that heterogeneous workload can severely impact the availability of IaaS clouds. Although previous work has investigated global queues, VM deployment, and failure of PMs, two aspects are yet to be fully explored: one is the impact of task size and the other is the differing features across PMs such as the variable execution rate and capacity. To address these challenges we propose an attribute-based availability model of large scale IaaS developed in the formal modeling language CARMA. The size of tasks in our model can be a fixed integer value or follow the normal, uniform or log-normal distribution. Additionally, our model also provides an easy approach to investigating how to arrange the slack and normal resources in order to achieve availability levels. The two goals of our work are providing an analysis of the availability of IaaS and showing that the use of CARMA allows us to easily model complex phenomena that were not readily captured by other existing approaches.

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Smoothed model checking based on Gaussian process classification provides a powerful approach for statistical model checking of parametric continuous time Markov chain models. The method constructs a model for the functional dependence of satisfaction probability on the Markov chain parameters. This is done via Gaussian process inference methods from a limited number of observations for different parameter combinations. In this work we consider extensions to smoothed model checking based on sparse variational methods and active learning. Both are used successfully to improve the scalability of smoothed model checking. In particular, we see that active learning-based ideas for iteratively querying the simulation model for observations can be used to steer the model-checking to more informative areas of the parameter space and thus improve sample efficiency. Online extensions of sparse variational Gaussian process inference algorithms are demonstrated to provide a scalable method for implementing active learning approaches for smoothed model checking.