A Numerical Algorithm for the Solution of Product-Form Models with Infinite State Spaces

  • Simonetta Balsamo
  • Gian-Luca Dei Rossi
  • Andrea Marin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6342)


Markovian models play a pivotal role in system performance evaluation field. Several high level formalisms are capable to model systems consisting of some interacting sub-models, but often the resulting underlying process has a number of states that makes the computation of the solution unfeasible. Product-form models consist of a set of interacting sub-models and have the property that their steady-state solution is the product of the sub-model solutions considered in isolation and opportunely parametrised. The computation of the steady-state solution of a composition of arbitrary and possibly different types of models in product-form is still an open problem. It consists of two parts: a) deciding whether the model is in product-form and b) in this case, compute the stationary distribution efficiently. In this paper we propose an algorithm to solve these problems that extends that proposed in [14] by allowing the sub-models to have infinite state spaces. This is done without a-priori knowledge of the structure of the stochastic processes underlying the model components. As a consequence, open models consisting of non homogeneous components having infinite state space (e.g., a composition of G-queues, G-queues with catastrophes, Stochastic Petri Nets with product-forms) may be modelled and efficiently studied.


State Space Reversed Rate Strong Connected Component First Come First Serve Jackson Network 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Simonetta Balsamo
    • 1
  • Gian-Luca Dei Rossi
    • 1
  • Andrea Marin
    • 1
  1. 1.Dipartimento di InformaticaUniversità Ca’ Foscari di VeneziaVeneziaItaly

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