Structured Solution of Asynchronously Communicating Stochastic Modules
IEEE Transactions on Software Engineering
Hierarchical Structuring of Superposed GSPNs
IEEE Transactions on Software Engineering
A Toolbox for the Analysis of Discrete Event Dynamic Systems
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
Efficient Reachability Set Generation and Storage Using Decision Diagrams
Proceedings of the 20th International Conference on Application and Theory of Petri Nets
Integrating Synchronization with Priority into a Kronecker Representation
TOOLS '00 Proceedings of the 11th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
Symbolic Methods for the State Space Exploration of GSPN Models
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
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We present a systematic discussion of algorithms to multiply a vector by a matrix expressed as the Kronecker product of sparse matrices, extending previous work in a unified notational framework. Then, we use our results to define new algorithms for the solution of large structured Markov models. In addition to a comprehensive overview of existing approaches, we give new results with respect to: (1) managing certain types of state-dependent behavior without incurring extra cost; (2) supporting both Jacobi-style and Gauss-Seidel-style methods by appropriate multiplication algorithms; (3) speeding up algorithms that consider probability vectors of size equal to the ``actual'''' state space instead of the ``potential'''' state space.