Performance models of multiprocessor systems
Performance models of multiprocessor systems
Transient analysis of acyclic markov chains
Performance Evaluation
Computing Poisson probabilities
Communications of the ACM
Numerical transient analysis of Markov models
Computers and Operations Research
Stochastic Automata Network of Modeling Parallel Systems
IEEE Transactions on Software Engineering
State space exploration in Markov models
SIGMETRICS '92/PERFORMANCE '92 Proceedings of the 1992 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
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)
Generalized Stochastic Petri Nets: A Definition at the Net Level and its Implications
IEEE Transactions on Software Engineering
PNPM '87 The Proceedings of the Second International Workshop on Petri Nets and Performance Models
Parallel State Space Exploration for GSPN Models
Proceedings of the 16th International Conference on Application and Theory of Petri Nets
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
Storage Alternatives for Large Structured State Spaces
Proceedings of the 9th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
ON THE USE OF KRONECKER OPERATORS FOR THE SOLUTION OF GENERALIZED STOCHASTIC PETRI NETS
ON THE USE OF KRONECKER OPERATORS FOR THE SOLUTION OF GENERALIZED STOCHASTIC PETRI NETS
Kronecker Algebra and (Stochastic) Petri Nets: Is It Worth the Effort?
ICATPN '01 Proceedings of the 22nd International Conference on Application and Theory of Petri Nets
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The paper considers transient analysis using randomization for superposed generalized stochastic Petri nets (GSPNs). Since state space explosion implies that space is the bottleneck for numerical analysis, superposed GSPNs profit from the structured representation known for its associated Markov chain. This moves the bottleneck for analysis from space for generator matrices to space for iteration vectors. Hence a variation of randomization is presented which allows to reduce space requirements for iteration vectors. An additional and welcome side effect is that during an initial phase, this algorithm avoids useless multiplications involving states with zero probability. Furthermore, it accommodates to adaptive randomization in a natural way. Although the algorithm has been developed for superposed GSPNs, it applies to continuous time Markov chains in a more general setting.