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On the Use of Structural Petri Net Analysis for Studying Product Form Equilibrium Distributions of Queueing Networks with Blocking

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Application and Theory of Petri Nets 1998 (ICATPN 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1420))

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Abstract

In this paper we investigate some relations between the Petri net formalism and the queueing networks with blocking. This type of queueing network models are used to represent systems with finite capacity resource constraints, such as production, communication and computer systems. Various blocking mechanisms have been defined in the literature to represent the different behaviours of real systems with limited resources.

We show that the representation of these queueing networks by means of Generalized Stochastic Petri Nets offers the possibility of using results developed within the Petri net framework. In particular, we investigate product form equilibrium distributions for queueing networks with blocking by means of structural Petri net results. More precisely, we use the notion of implicit places. With this concept we characterise a class of queueing networks with blocking having interesting properties. For each queueing network of this class there exists another model with the same performance measures and exhibiting product form equilibrium distribution.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Torino, corso Svizzera 185, 10149, Torino, Italy

    Marco Gribaudo & Matteo Sereno

Authors
  1. Marco Gribaudo
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  2. Matteo Sereno
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Editor information

Editors and Affiliations

  1. Institut AIFB, University of Karlsruhe, D-76128, Karlsruhe, Germany

    Jörg Desel

  2. Departamento de Informatica a Ingenieria de Sistemas Centro Politecnico Superior, Universidad de Zaragoza, c/ Maria de Luna, 3, E-50015, Zaragoza, Spain

    Manuel Silva

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© 1998 Springer-Verlag Berlin Heidelberg

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Gribaudo, M., Sereno, M. (1998). On the Use of Structural Petri Net Analysis for Studying Product Form Equilibrium Distributions of Queueing Networks with Blocking. In: Desel, J., Silva, M. (eds) Application and Theory of Petri Nets 1998. ICATPN 1998. Lecture Notes in Computer Science, vol 1420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69108-1_14

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  • DOI: https://doi.org/10.1007/3-540-69108-1_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64677-8

  • Online ISBN: 978-3-540-69108-2

  • eBook Packages: Springer Book Archive

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