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Réseaux d'Automates Stochastiques : Analyse transitoire en temps continu et algèbre tensorielle pour une sémantique en temps discret

Leonardo Brenner 1, 2
2 MESCAL - Middleware efficiently scalable
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
Abstract : This thesis presents methods and algorithms for the performance evaluation of large state space models described by high-level formalisms. Among the various formalisms commonly used we use Stochastic Automata Networks (SAN) formalism. SAN formalism is characterized by the representation of very large systems by the composition of its subsystems (automata), where these automata interact with each other by synchronizing events or rates and functional probabilities.

The first part of this thesis focuses on the computation of transient performance indices for large models. When we compute transient indices, such as point availability, the uniformisation method is often used. However, the number of iterations (vector-matrix multiplication) can be very large, which is critical for very large models. Stationnarity detection methods can reduce the computational cost by stopping the iterations when the steady state is reached. In this thesis, we propose an adaptation and a comparison of the different stationnarity detection methods when the matrix is stored in a tensor format. The methods are compared using two criteria: number of iterations and results accuracy.

In the second part, we present the SAN formalism for discrete time models. The SAN formalism formal definition presented in this thesis allows us to define the semantic of discrete time models that we wish to explore. We define a new tensor algebra (called Complex Tensor Algebra - XTA) capable of expressing this semantic. For that uses, three operators are defined to describe the different behavior of a system, such as simultaneity, competition and choice. Finally, the main contribution of this thesis lies in the definition of a tensor formula (called discrete descriptor) that uses this new algebra to describe a discrete time SAN model in a compact mode. We show that this discrete descriptor can easily generate the Markov chain represented by the SAN model.
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Contributor : Leonardo Brenner <>
Submitted on : Friday, November 13, 2009 - 11:07:26 AM
Last modification on : Tuesday, February 9, 2021 - 3:18:03 PM
Long-term archiving on: : Saturday, November 26, 2016 - 2:34:00 PM


  • HAL Id : tel-00424652, version 2



Leonardo Brenner. Réseaux d'Automates Stochastiques : Analyse transitoire en temps continu et algèbre tensorielle pour une sémantique en temps discret. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 2009. Français. ⟨tel-00424652v2⟩



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