Theoretical Computer Science
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
Beyond Memoryless Distributions: Model Checking Semi-Markov Chains
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Model-Checking for Probabilistic Real-Time Systems (Extended Abstract)
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
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
Verifying Automata Specifications of Probabilistic Real-time Systems
Proceedings of the Real-Time: Theory in Practice, REX Workshop
Probabilistic Verification of Discrete Event Systems Using Acceptance Sampling
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
How to Specify and Verify the Long-Run Average Behavior of Probabilistic Systems
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
The DSPNexpress 2.000 Performance and Dependability Modeling Environment
FTCS '99 Proceedings of the Twenty-Ninth Annual International Symposium on Fault-Tolerant Computing
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Logic and stochastic modeling with SMART
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
Markov Chains and Stochastic Stability
Markov Chains and Stochastic Stability
A theory of stochastic systems part I: Stochastic automata
Information and Computation
Symbolic analysis for GSMP models with one stateful clock
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Stochastic Petri Nets: Modelling, Stability, Simulation
Stochastic Petri Nets: Modelling, Stability, Simulation
Measuring performance of continuous-time stochastic processes using timed automata
Proceedings of the 14th international conference on Hybrid systems: computation and control
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
Bounded model checking for GSMP models of stochastic real-time systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
On time-average limits in deterministic and stochastic petri nets
Proceedings of the 4th ACM/SPEC International Conference on Performance Engineering
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We study long run average behavior of generalized semi-Markov processes with both fixed-delay events as well as variable-delay events. We show that allowing two fixed-delay events and one variable-delay event may cause an unstable behavior of a GSMP. In particular, we show that a frequency of a given state may not be defined for almost all runs (or more generally, an invariant measure may not exist). We use this observation to disprove several results from literature. Next we study GSMP with at most one fixed-delay event combined with an arbitrary number of variable-delay events. We prove that such a GSMP always possesses an invariant measure which means that the frequencies of states are always well defined and we provide algorithms for approximation of these frequencies. Additionally, we show that the positive results remain valid even if we allow an arbitrary number of reasonably restricted fixed-delay events.