ACM Transactions on Computer Systems (TOCS)
Theoretical Computer Science
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
Iterative analysis of Markov regenerative models
Performance Evaluation
Probability and statistics with reliability, queuing and computer science applications
Probability and statistics with reliability, queuing and computer science applications
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
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
Towards Model Checking Stochastic Process Algebra
IFM '00 Proceedings of the Second International Conference on Integrated Formal Methods
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
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
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
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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
The ins and outs of the probabilistic model checker MRMC
Performance Evaluation
Efficient CTMC model checking of linear real-time objectives
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
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In this paper we investigate the computation, and the stochastic interpretation, of backward probabilities of Markov chains (transient and steady-state probabilities derived from backward Kolmogorov equations) and its extension to the case of Markov Regenerative Processes (MRP). The study is then extended to the case of non-ergodic settings, which enlights a substantial difference between the forward solution process (based on forward Kolmogorov equations) and the backward one. We shall clarify the role that backward solutions play in computing absorption probabilities and in the model-checking of stochastic logics as CSL and CSLTA, which typically require the steady state solution of a non-ergodic CTMC and MRP respectively. Moreover we show that the algorithm for the computation of the whole set of states that satisfy a CSL formula, which is standard practice in CSL model-checkers, can be seen as a case of computation of backward probabilities of Continuous Time Markov Chains (CTMCs). The backward computation of MRP is then inserted in the context of matrix-free solution technique, which allows to deal with MRP of much bigger size than the standard approach based on the computation and solution of the embedded Markov chain.