Service stage Petri net models with product form solution
Queueing Systems: Theory and Applications
A methodology for solving Markov models of parallel systems
Journal of Parallel and Distributed Computing
Markovian Petri Nets protocols with product form solution
Performance Evaluation
Efficient descriptor-vector multiplications in stochastic automata networks
Journal of the ACM (JACM)
Computer Networks and Systems: Queueing Theory and Performance Evaluation
Computer Networks and Systems: Queueing Theory and Performance Evaluation
IEEE Transactions on Software Engineering
International Workshop on Timed Petri Nets
On the benefits of using functional transitions and Kronecker algebra
Performance Evaluation
Product Form Steady-State Distribution for Stochastic Automata Networks with Domino Synchronizations
EPEW '08 Proceedings of the 5th European Performance Engineering Workshop on Computer Performance Engineering
Stochastic Automata Networks with Master/Slave Synchronization: Product Form and Tensor
ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
Short communication: Product-forms and functional rates
Performance Evaluation
Response time distributions and network perturbation into product-form
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Complex synchronizations in Markovian models: a tensor-based proof of product form
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Collaboration of discrete-time Markov chains: Tensor and product form
Performance Evaluation
Markovian queueing network with complex synchronizations: Product form and tensor
Performance Evaluation
Lumping and reversed processes in cooperating automata
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
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We consider Stochastic Automata Networks (SAN) in continuous time and we prove a sufficient condition for the steady-state distribution to have product form. We consider SAN without synchronizations where the transitions of one automaton may depend of the states of the other automata. Even with this restriction, this sufficient condition is quite simple and this theorem generalizes former results on SAN but also on modulated Markovian queues, such as the Boucherie's theory on competing Markov chain, or on reversible queues considered by Kelly. The sufficient condition and the proof are purely algebraic.