Computing Poisson probabilities
Communications of the ACM
The Effect of Execution Policies on the Semantics and Analysis of Stochastic Petri Nets
IEEE Transactions on Software Engineering
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
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
TimeNET: a toolkit for evaluating non-Markovian stochastic Petri nets
Performance Evaluation - Special issue: performance modeling tools
A Characterization of the Stochastic Process Underlying a Stochastic Petri Net
IEEE Transactions on Software Engineering
Expected Impulsive Rewards in Markov Regenerative Stochastic Petri Nets
Proceedings of the 17th International Conference on Application and Theory of Petri Nets
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
Transient Analysis of Deterministic and Stochastic Petri Nets
Proceedings of the 14th International Conference on Application and Theory of Petri Nets
Transient Analysis of Deterministic and Stochastic Petri Nets with TimeNET
MMB '95 Proceedings of the 8th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation: Quantitative Evaluation of Computing and Communication 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
Steady State Solution of MRSPN with Mixed Preemption Policies
IPDS '96 Proceedings of the 2nd International Computer Performance and Dependability Symposium (IPDS '96)
New results for the analysis of deterministic and stochastic Petri nets
IPDS '95 Proceedings of the International Computer Performance and Dependability Symposium on Computer Performance and Dependability Symposium
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
Quantitative system evaluation with DSPNexpress 2000
Proceedings of the 2nd international workshop on Software and performance
Petri Net Modelling and Performability Evaluation with TimeNET 3.0
TOOLS '00 Proceedings of the 11th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
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This paper presents an efficient and numerically reliable method for the transient analysis of deterministic and stochastic Petri nets. The transient behavior is described by state equations derived by the method of supplementary variables. Significant features of the proposed solution algorithm of fourth order are an automatic stepsize control and a two-stage relative error control. Furthermore, a formal way of dealing with discontinuities in the transient state equations is developed. This resolves the problems posed by initially enabled deterministic transitions and also improves the accuracy of numerical results. Experiments with a queuing system with failure and repair illustrate the efficiency (with respect to both CPU-time and memory space) and the numerical quality of the new algorithm.