Complex synchronizations in Markovian models: a tensor-based proof of product form

Authors:
T. H. Dao Thi;J. M. Fourneau
Affiliations:
Université de Versailles St-Quentin, Versailles, France;Université de Versailles St-Quentin, Versailles, France
Venue:
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Year:
2009

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Abstract

We consider complex synchronizations in a generalized network of queues with signals (Gnetwork) or Stochastic Automata Networks without functions. Both models allow to describe their continuous time Markov chain as a summation of tensor (or Kronecker) products and sums of local description of queues (or automata). We give a purely algebraic proof of the product form results based on properties of the tensor products. These results generalizes many well-known results in queueing theory but also on all the models which allow a tensor based representation such as Stochastic Petri Nets or Stochastic Process Algebra.