The Effect of Execution Policies on the Semantics and Analysis of Stochastic Petri Nets
IEEE Transactions on Software Engineering
The mathematics of Petri nets
Generalization of Queueing Network Product Form Solutions to Stochastic Petri Nets
IEEE Transactions on Software Engineering
Markovian Petri Nets protocols with product form solution
Performance Evaluation
Free choice Petri nets
Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets
Performance Evaluation
On the Product Form Solution for Stochastic Petri Nets
Proceedings of the 13th International Conference on Application and Theory of Petri Nets
Product-form and stochastic Petri nets: a structural approach
Performance Evaluation
Synthesis and analysis of product-form petri nets
PETRI NETS'11 Proceedings of the 32nd international conference on Applications and theory of Petri Nets
Hierarchically constructed Petri-nets and product-forms
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Methodological construction of product-form stochastic Petri nets for performance evaluation
Journal of Systems and Software
Analysis of stochastic Petri nets with signals
Performance Evaluation
Operational semantics for product-form solution
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Operational semantics for product-form solution
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
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Consider a Markovian Petri net with race policy. The marking process has a "product form" stationary distribution if the probability of viewing a given marking can be decomposed as the product over places of terms depending only on the local marking. First we observe that the Deficiency Zero Theorem of Feinberg, developped for chemical reaction networks, provides a structural and simple sufficient condition for the existence of a product form. In view of this, we study the classical subclass of bounded free-choice nets. Roughly, we show that the only such Petri nets having a product form are the state machines which can alternatively be viewed as Jackson networks.