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Skipping and Fetching: Insights on Non-conventional Product-Form Solutions

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Quantitative Evaluation of Systems (QEST 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14287))

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Abstract

Complex models of computer systems are often difficult to study with numerical or analytical approaches because of the state space explosion problem. The class of product-form models is one of the most significant tools for overcoming this problem, and in many applications, this tool is the only way to perform a quantitative analysis.

In this paper, we study the duality between two different product-form models. The first consists of a queuing network with finite capacity waiting rooms governed by the skip-over policy. The second is a recently presented product-form model in which a job fetching policy is applied. To investigate the relationships between these two models, we first extend the fetching queuing model to allow for finite capacity warehouses and for a Repetitive Service Blocking with Random Destination (RS-RD) discipline. Subsequently, we represent their distinctive features in terms of Generalized Stochastic Petri Nets which precisely specify their semantics in a modular manner and provide clear and intuitive interpretations of these policies. With these two preliminary results, we prove that it is possible to structurally transform a model of one class into one of the other and vice versa, thus choosing the representation that is computationally more convenient to compute the performance measures of interest.

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Notes

  1. 1.

    How to deal with cycles of immediate transitions is described in the original GSPN paper [2], discussed in details in [11], and implemented in SMART [10].

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Acknowledgements

This work has been partially supported by project INdAM-GNCS 2023 RISICO CUP E53C22001930001.

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Authors and Affiliations

  1. Università Ca’ Foscari Venezia, Venice, Italy

    Diletta Olliaro & Andrea Marin

  2. Università di Torino, Turin, Italy

    Gianfranco Balbo & Matteo Sereno

Authors
  1. Diletta Olliaro
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  2. Gianfranco Balbo
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  3. Andrea Marin
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  4. Matteo Sereno
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Correspondence to Diletta Olliaro .

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Editors and Affiliations

  1. Radboud University Nijmegen, Nijmegen, The Netherlands

    Nils Jansen

  2. IMT Lucca, Lucca, Italy

    Mirco Tribastone

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Olliaro, D., Balbo, G., Marin, A., Sereno, M. (2023). Skipping and Fetching: Insights on Non-conventional Product-Form Solutions. In: Jansen, N., Tribastone, M. (eds) Quantitative Evaluation of Systems. QEST 2023. Lecture Notes in Computer Science, vol 14287. Springer, Cham. https://doi.org/10.1007/978-3-031-43835-6_8

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  • DOI: https://doi.org/10.1007/978-3-031-43835-6_8

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