Research Article
Complex Synchronizations in Markovian Models: a Tensor-based Proof of Product Form
@INPROCEEDINGS{10.4108/ICST.VALUETOOLS2009.7507, author={T. H. Dao Thi and J.M. Fourneau}, title={Complex Synchronizations in Markovian Models: a Tensor-based Proof of Product Form}, proceedings={4th International ICST Conference on Performance Evaluation Methodologies and Tools}, publisher={ICST}, proceedings_a={VALUETOOLS}, year={2010}, month={5}, keywords={Product form Markovian Networks of Queues Tensor Algebra}, doi={10.4108/ICST.VALUETOOLS2009.7507} }- T. H. Dao Thi
J.M. Fourneau
Year: 2010
Complex Synchronizations in Markovian Models: a Tensor-based Proof of Product Form
VALUETOOLS
ICST
DOI: 10.4108/ICST.VALUETOOLS2009.7507
Abstract
We consider complex synchronizations in a generalized net- work of queues with signals (Gnetwork) or Stochastic Au- tomata 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 descrip- tion 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.
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