Introduction to queueing networks
Introduction to queueing networks
Numerical Analysis of Superposed GSPNs
IEEE Transactions on Software Engineering - Special issue: best papers of the sixth international workshop on Petri nets and performance models (PNPM'95)
Efficient descriptor-vector multiplications in stochastic automata networks
Journal of the ACM (JACM)
An efficient disk-based tool for solving large Markov models
Performance Evaluation - Special issue on tools for performance evaluation
Modelling with Generalized Stochastic Petri Nets
ACM SIGMETRICS Performance Evaluation Review - Special issue on Stochastic Petri Nets
Modeling Using Stochastic Reward Nets
MASCOTS '93 Proceedings of the International Workshop on Modeling, Analysis, and Simulation On Computer and Telecommunication Systems
On Combining Functional Verification and Performance Evaluation Using CADP
FME '02 Proceedings of the International Symposium of Formal Methods Europe on Formal Methods - Getting IT Right
Reachability Analysis Based on Structured Representations
Proceedings of the 17th International Conference on Application and Theory of Petri Nets
Superposed Generalized Stochastic Petri Nets: Definition and Efficient Solution
Proceedings of the 15th International Conference on Application and Theory of Petri Nets
INFORMS Journal on Computing
"On-the-fly" Soltuion Techniques for Stochastic Petri Nets and Extensions
PNPM '97 Proceedings of the 6th International Workshop on Petri Nets and Performance Models
Hierarchical Structuring of Superposed GSPNs
PNPM '97 Proceedings of the 6th International Workshop on Petri Nets and Performance Models
A Data Structure for the Efficient Kronecker Solution of GSPNs
PNPM '99 Proceedings of the The 8th International Workshop on Petri Nets and Performance Models
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Memory-Efficient Kronecker Algorithms with Applications to the Modelling of Parallel Systems
IPDPS '03 Proceedings of the 17th International Symposium on Parallel and Distributed Processing
Efficient Solution of GSPNs Using Canonical Matrix Diagrams
PNPM '01 Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM'01)
On the benefits of using functional transitions and Kronecker algebra
Performance Evaluation
Performance modelling and Markov chains
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
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We present a new algorithm for computing the solution of large Markov chain models whose generators can be represented in the form of a generalized tensor algebra, such as networks of stochastic automata. The tensor structure inherently involves a product state space but, inside this product state space, the actual reachable state space can be much smaller. For such cases, we propose an improvement of the standard numerical algorithm, the so-called "shuffle algorithm", which necessitates only vectors of the size of the actual state space. With this contribution, numerical algorithms based on tensor products can now handle larger models.