Explicit Model Checking of Very Large MDP using Partitioning and Secondary Storage

The applicability of model checking is hindered by the state space explosion problem in combination with limited amounts of main memory. To extend its reach, the large available capacities of secondary storage such as hard disks can be exploited. Due to the specific performance characteristics of secondary storage technologies, specialised algorithms are required. In this paper, we present a technique to use secondary storage for probabilistic model checking of Markov decision processes. It combines state space exploration based on partitioning with a block-iterative variant of value iteration over the same partitions for the analysis of probabilistic reachability and expected-reward properties. A sparse matrix-like representation is used to store partitions on secondary storage in a compact format. All file accesses are sequential, and compression can be used without affecting runtime. The technique has been implemented within the Modest Toolset. We evaluate its performance on several benchmark models of up to 3.5 billion states. In the analysis of time-bounded properties on real-time models, our method neutralises the state space explosion induced by the time bound in its entirety.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-24953-7_1

Towards Stochastic FMI Co-Simulations: Implementation of an FMU for a Stochastic Activity Networks Simulator

The advantage of co-simulation with respect to traditional single-paradigm simulation lies mainly in the modeling flexibility it affords in composing large models out of submodels, each expressed in the most appropriate formalism. One aspect of this flexibility is the modularity of the co-simulation framework, which allows developers to replace each sub-model with a new version, possibly based on a different formalism or a different simulator, without changing the rest of the co- simulation. This paper reports on the replacement of a sub-model in a co-simulation built on the INTO-CPS framework. Namely, an existing co-simulation of a water tank, available in the INTO-CPS distribution, has been modified by replacing the tank sub-model with a sub-model built as a Stochastic Activity Network simulated on Möbius, a tool used to perform statistical analyses of systems with stochastic behavior. This work discusses aspects of this redesign, including the necessary modifications to the Möbius sub-model. In this still preliminary work, the Stochastic Activity Network features related to stochastic models have not been used, but a simple deterministic model has proved useful in indicating an approach to the integration of Stochastic Activity Networks into a co-simulation framework

Evaluation of Iterative Methods on Large Markov Chains Generated by GSPN Models

GSPN models often generate high cardinality state spaces, whose analysis requires the solution of very large and sparse nonsymmetric linear systems for the associated Markov chain. In this paper we report the results of an empirical investigation of three well-known iterative methods for linear systems of equations: Gauss-Seidel, GMRES, and Bi-CGstab. We evaluate these methods on several large Markov chains generated by GSPN models proposed in the literature. Issues addressed include state space characterization, problem conditioning, numerical accuracy and stability, and computation time. Results show that increased attention should be paid to the numerical issues underlying performance and reliability analyses when dealing with large state spaces