ACM Transactions on Computer Systems (TOCS)
Computing Poisson probabilities
Communications of the ACM
Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
Iterative analysis of Markov regenerative models
Performance Evaluation
Performance Analysis of Communication Systems with Non-Markovian Stochastic Petri Nets
Performance Analysis of Communication Systems with Non-Markovian Stochastic Petri Nets
Performance Modelling with Deterministic and Stochostic Petri Nets
Performance Modelling with Deterministic and Stochostic Petri Nets
Markov Regenerative Stochastic Petri Nets to Model and Evaluate Phased Mission Systems Dependability
IEEE Transactions on Computers
Faster and Symbolic CTMC Model Checking
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
On Petri nets with deterministic and exponentially distributed firing times
Advances in Petri Nets 1987, covers the 7th European Workshop on Applications and Theory of Petri Nets
DEEM: A Tool for the Dependability Modeling and Evaluation of Multiple Phased Systems
DSN '00 Proceedings of the 2000 International Conference on Dependable Systems and Networks (formerly FTCS-30 and DCCA-8)
Dependability Modeling and Evaluation of Phased Mission Systems: A DSPN Approach
DCCA '99 Proceedings of the conference on Dependable Computing for Critical Applications
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Introduction to Discrete Event Systems
Introduction to Discrete Event Systems
Depth-first search and linear grajh algorithms
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
Model Checking Timed and Stochastic Properties with CSL^{TA}
IEEE Transactions on Software Engineering
PRISM: probabilistic model checking for performance and reliability analysis
ACM SIGMETRICS Performance Evaluation Review
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
DTMC Model Checking by SCC Reduction
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
DSPN-Tool: A New DSPN and GSPN Solver for GreatSPN
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
MC4CSLTA: An Efficient Model Checking Tool for CSLTA
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
A component-based solution method for non-ergodic Markov regenerative processes
EPEW'10 Proceedings of the 7th European performance engineering conference on Computer performance engineering
Numerical analysis of rational processes beyond Markov chains
Performance Evaluation
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Irreducible Markov Regenerative Processes (MRPs) are solved by either building and storing the embedded DTMC (EMC) beforehand (explicit approach), or by applying implicit techniques, in which the EMC is never computed or stored. The implicit approach usually outperforms the explicit one, both in terms of time and memory. This paper introduces an implicit and component-based method for the steady-state solution of reducible Markov regenerative processes: the strongly connected components of the characteristic matrices of the process are used to identify a structure of components that is exploited by the solution process to discriminate components of the process that have a simple or a complex structure, and corresponding lower and higher solution costs. The solution then considers one component at a time, applying to each of them the simplest solution technique adequate to the actual component complexity. An implicit approach is followed, which saves the cost of building and storing the EMC, but makes non trivial the identification of the strongly connected components. The paper shows the efficacy of the method both in theory and on a set of MRPs arising from queueing networks, stochastic Petri nets and from the stochastic model checking of Markov chains. In particular it is shown that the cost of the model checking of the Until formula of the stochastic logic CSL^T^A reduces to that of CSL if the component method is used.