Advances in Model Representations
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Out-of-Core Solution of Large Linear Systems of Equations Arising from Stochastic Modelling
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Implicit GSPN reachability set generation using decision diagrams
Performance Evaluation - Dependable systems and networks-performance and dependability symposium (DSN-PDS) 2002: Selected papers
Model-Based Evaluation: From Dependability to Security
IEEE Transactions on Dependable and Secure Computing
On the benefits of using functional transitions and Kronecker algebra
Performance Evaluation
Logic and stochastic modeling with SMART
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
Memory-efficient Kronecker algorithms with applications to the modelling of parallel systems
Future Generation Computer Systems - Systems performance analysis and evaluation
Analysis of Markov reward models using zero-suppressed multi-terminal BDDs
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Saturation for a General Class of Models
IEEE Transactions on Software Engineering
Approximating stationary measures of structured continuous-time Markov models using matrix diagrams
ACM SIGMETRICS Performance Evaluation Review
Split: a flexible and efficient algorithm to vector-descriptor product
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Advanced features in SMART: the stochastic model checking analyzer for reliability and timing
ACM SIGMETRICS Performance Evaluation Review
Data representation and efficient solution: a decision diagram approach
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
A framework to decompose GSPN models
ICATPN'05 Proceedings of the 26th international conference on Applications and Theory of Petri Nets
EPEW'05/WS-FM'05 Proceedings of the 2005 international conference on European Performance Engineering, and Web Services and Formal Methods, international conference on Formal Techniques for Computer Systems and Business Processes
Efficient vector-descriptor product exploiting time-memory trade-offs
ACM SIGMETRICS Performance Evaluation Review
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Abstract: The solution of a generalized stochastic Petri net (GSPN) is severely restricted by the size of its underlying continuous-time Markov chain. In recent work, matrix diagrams built from a Kronecker expression for the transition rate matrix of certain types of GSPNs were shown to allow for more efficient solution; however, the GSPN model requires a special form, so that the transition rate matrix has a Kronecker expression. In this paper, we extend the earlier results to GSPN models with partitioned sets of places. Specifically, we give a more restrictive definition for matrix diagrams and show that the new form is canonical. We then present an algorithm that builds a canonical matrix diagram representation for an arbitrary non-negative matrix, given encodings for the sets of rows and columns. Using this algorithm, a Kronecker expression is not required to construct the matrix diagram. The efficient matrix diagram algorithms for numerical solution presented earlier are still applicable. We apply our technique to several example GSPNs.