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We show how some graph theoretical arguments may be used to reduce the complexity of the computation of the steady-state distribution of Markov chain. We consider the directed graph associated to a Markov chain derived from a Stochastic Automata Network (SAN). The structural properties of the automata are used to establish new various results. First, we… (More)

We consider multiple class G-networks of processor sharing queues with negative customers which destroy all the customers in a queue. We prove that these networks have a product form solution for steady-state distribution. These networks may have some applications in reliability or performability as the negative customers may clearly model breakdown of… (More)

We present X-Bounds, a new tool to implement a methodology based on stochastic ordering, algorithmic derivation of simpler Markov chains and numerical analysis of these chains. The performance indices defined by reward functions are stochastically bounded by reward functions computed on much simpler or smaller Markov chains obtained after aggregation or… (More)

We present an algorithm for automatically predicting the topological family of any RNA three-way junction, given only the information from the secondary structure: the sequence and the Watson-Crick pairings. The parameters of the algorithm have been determined on a data set of 33 three-way junctions whose 3D conformation is known. We applied the algorithm… (More)

We present a new type of multiclass generalized networks of queues with a steady-state product form solution. At its arrival into a queue, a negative customer (or a signal) starts an iteration. At each step of the iteration, a customer is deleted according to a probability which may depend on the type of customer. The iteration stops when the deletion… (More)

- J M Fourneau, L Kloul, L Mokdad, F Quessette
- 1994

We present a new performance evaluation tool based on the analysis of large Markov chains and Stochastic Automata Networks. Using some graph theoretical arguments, we show how to systematically perform state reduction. The graph properties can be checked easily because we take advantage of the tensorial construction of the Markov chain from the Stochastic… (More)

To be published in "Les Annales des télécommunications "(CNET, PPUR) Abstract The Stochastic Automata Networks formalism is an attractive technique to model complex systems with interacting components. Each component of the system is modelled by a single automaton; interactions between components are modelled by labels on the arcs which may represent… (More)