Stochastic Petri Net Representation of Discrete Event Simulations
IEEE Transactions on Software Engineering
Modeling and Verification of Time Dependent Systems Using Time Petri Nets
IEEE Transactions on Software Engineering
Analysis of stochastic Petri nets by the method of supplementary variables
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Markov regenerative stochastic Petri nets
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
Static Analysis and Dynamic Steering of Time-Dependent Systems
IEEE Transactions on Software Engineering
A Characterization of the Stochastic Process Underlying a Stochastic Petri Net
IEEE Transactions on Software Engineering
Timing Assumptions and Verification of Finite-State Concurrent Systems
Proceedings of the International Workshop on Automatic Verification Methods for Finite State Systems
Transient analysis of Markov regenerative stochastic Petri nets: a comparison of approaches
PNPM '95 Proceedings of the Sixth International Workshop on Petri Nets and Performance Models
PNPM '99 Proceedings of the The 8th International Workshop on Petri Nets and Performance Models
Markov regenerative SPN with non-overlapping activity cycles
IPDS '95 Proceedings of the International Computer Performance and Dependability Symposium on Computer Performance and Dependability Symposium
IPDS '95 Proceedings of the International Computer Performance and Dependability Symposium on Computer Performance and Dependability Symposium
Introducing Probability within State Class Analysis of Dense-Time-Dependent Systems
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Using Stochastic State Classes in Quantitative Evaluation of Dense-Time Reactive Systems
IEEE Transactions on Software Engineering
QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
Oris: a tool for modeling, verification and evaluation of real-time systems
International Journal on Software Tools for Technology Transfer (STTT)
Transient Analysis of Generalised Semi-Markov Processes Using Transient Stochastic State Classes
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
A framework for simulation and symbolic state space analysis of non-markovian models
SAFECOMP'11 Proceedings of the 30th international conference on Computer safety, reliability, and security
Non-markovian analysis for model driven engineering of real-time software
Proceedings of the 4th ACM/SPEC International Conference on Performance Engineering
Transient analysis of networks of stochastic timed automata using stochastic state classes
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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The method of stochastic state classes approaches the analysis of Generalised Semi Markov Processes (GSMPs) through the symbolic derivation of probability density functions over supports described by Difference Bounds Matrix (DBM) zones. This makes steady state analysis viable, provided that at least one regeneration point is visited by every cyclic behaviour of the model. We extend the approach providing a way to derive transient probabilities. To this end, stochastic state classes are extended with a supplementary timer that enables the symbolic derivation of the distribution of time at which a class can be entered. The approach is amenable to efficient implementation when model timings are given by expolynomial distributions, and it can be applied to perform transient analysis of GSMPs within any given time bound. In the special case of models underlying a Markov Regenerative Process (MRGP), the method can also be applied to the symbolic derivation of local and global kernels, which in turn provide transient probabilities through numerical integration of generalised renewal equations. Since much of the complexity of this analysis is due to the local kernel, we propose a selective derivation of its entries depending on the specific transient measure targeted by the analysis.