4th International ICST Conference on Performance Evaluation Methodologies and Tools

Research Article

Complex Synchronizations in Markovian Models: a Tensor-based Proof of Product Form

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  • @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
T. H. Dao Thi1,*, J.M. Fourneau1,*
  • 1: PRiSM CNRS UMR 8144, Université de Versailles St-Quentin, UniverSud, 45 Av. des Etats Unis, 78000 Versailles, France
*Contact email: thu-ha.dao-thi@prism.uvsq.fr, jmf@prism.uvsq.fr

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.