Product Form Steady-State Distribution for Stochastic Automata Networks with Domino Synchronizations

Authors:
Jean-Michel Fourneau
Affiliations:
PRiSM, Université de Versailles-Saint-Quentin, CNRS, UniverSud, Versailles, France and INRIA Projet Mescal, LIG, CNRS, Montbonnot, France
Venue:
EPEW '08 Proceedings of the 5th European Performance Engineering Workshop on Computer Performance Engineering
Year:
2008

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Abstract

We present a new kind of synchronization which allows Continuous Time Stochastic Automata Networks (SAN) to have a product form steady-state distribution. Unlike previous models on SAN with product form solutions, our model allows synchronization between three automata but functional rates are not allowed. The synchronization is not the usual "Rendez-Vous" but an ordered list of transitions. Each transition may fail. When a transition fails, the synchronization ends but all the transitions already executed are kept. This synchronization is related to the triggered customer movement between queues in a network and this class of SAN is a generalization of Gelenbe's networks with triggered customer movement.