Computing Poisson probabilities
Communications of the ACM
Analysis of large stochastic petri net models
Analysis of large stochastic petri net models
A decomposition approach for stochastic reward net models
Performance Evaluation
Principles of Discrete Event Simulation
Principles of Discrete Event Simulation
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Stochastic activity networks: formal definitions and concepts
Lectures on formal methods and performance analysis
Stochastic Well-Formed Colored Nets and Symmetric Modeling Applications
IEEE Transactions on Computers
The Möbius Framework and Its Implementation
IEEE Transactions on Software Engineering
Superposed Generalized Stochastic Petri Nets: Definition and Efficient Solution
Proceedings of the 15th International Conference on Application and Theory of Petri Nets
A Data Structure for the Efficient Kronecker Solution of GSPNs
PNPM '99 Proceedings of the The 8th International Workshop on Petri Nets and Performance Models
Optimal state-space lumping in Markov chains
Information Processing Letters
Adaptive decomposition and approximation for the analysis of stochastic petri nets
Performance Evaluation - Dependable systems and networks-performance and dependability symposium (DSN-PDS) 2002: Selected papers
Dependability Checking with StoCharts: Is Train Radio Reliable Enough for Trains?
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Lumping Matrix Diagram Representations of Markov Models
DSN '05 Proceedings of the 2005 International Conference on Dependable Systems and Networks
Process Algebras for Quantitative Analysis
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
A time-dependent extension of gillespie algorithm for biochemical stochastic π-calculus
Proceedings of the 2006 ACM symposium on Applied computing
Petri Net Based Descriptions for Systematic Understanding of Biological Pathways
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Dependability Analysis with Markov Chains: How Symmetries Improve Symbolic Computations
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
Bioinformatics
Interactive Markov chains: and the quest for quantified quality
Interactive Markov chains: and the quest for quantified quality
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
How might petri nets enhance your systems biology toolkit
PETRI NETS'11 Proceedings of the 32nd international conference on Applications and theory of Petri Nets
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Mathematical models of Ca2+ release sites derived from Markov chain models of intracellular Ca2+ channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic Ca2+ excitability (i.e., puffs and sparks). Ca2+ release site models are composed of a number of individual channel models whose dynamic behavior depends on the local Ca2+ concentration which is influenced by the state of all channels. We consider this application area to illustrate how stochastic Petri nets and in particular stochastic activity networks can be used to model dynamical phenomena in cell biology. We highlight how state-sharing composition operations as supported by the Möbius framework can represent both mean-field and spatial coupling assumptions in a natural manner. We investigate how state-of-the-art techniques for the numerical and simulative analysis of Markov chains associated with stochastic Petri nets scale when modeling Ca2+ signaling complexes of physiological size and complexity.