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Probabilistic Timed Graph Transformation Systems

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Graph Transformation (ICGT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10373))

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Abstract

Today, software has become an intrinsic part of complex distributed embedded real-time systems. The next generation of embedded real-time systems will interconnect the today unconnected systems via complex software parts and the service-oriented paradigm. Therefore besides timed behavior and probabilistic behavior also structure dynamics, where the architecture can be subject to changes at run-time, e.g. when dynamic binding of service end-points is employed or complex collaborations are established dynamically, is required. However, a modeling and analysis approach that combines all these necessary aspects does not exist so far.

To fill the identified gap, we propose Probabilistic Timed Graph Transformation Systems (PTGTSs) as a high-level description language that supports all the necessary aspects of structure dynamics, timed behavior, and probabilistic behavior. We introduce the formal model of PTGTSs in this paper and present a mapping of models with finite state spaces to probabilistic timed automata (PTA) that allows to use the PRISM model checker to analyze PTGTS models with respect to PTCTL properties.

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Notes

  1. 1.

    An alternative approach for graph transformation systems with time was developed in [11]. However, this approach is not suitable in our context since symbolic state space representations and quantitative analysis methods are not considered in [11].

  2. 2.

    Also stochastic graph transformation systems (SGTSs) [13] that incorporate stochastic timed behavior into GTSs by including continuous-time probability distributions that describe the average delay of firing of rules, once they are enabled, have been proposed. However, note that they do neither support probabilistic behavior nor real-time behavior as they assume a different model of time.

  3. 3.

    For an arbitrary set M, \(2_{\mathrm {fn}}^{M} \) denotes the set of finite nonempty subsets of M.

  4. 4.

    \( rhs (\rho )\) denotes the right-hand side of the rule \(\rho \).

  5. 5.

    For the priority function it holds that the higher the number assigned to a rule the higher is the priority of the rule.

  6. 6.

    For morphisms between clocks we omit the restricted notation and use the unrestricted notation to simplify the representation.

  7. 7.

    The range of the considered probabilities for non-successful connection attempts has been taken from [20] where for close range communication and high data rates an error rate of at most 13% has been observed for wireless communication.

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Authors and Affiliations

  1. Hasso Plattner Institute at the University of Potsdam, Potsdam, Germany

    Maria Maximova & Holger Giese

  2. SAP SE, Potsdam, Germany

    Christian Krause

Authors
  1. Maria Maximova
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  2. Holger Giese
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  3. Christian Krause
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Corresponding author

Correspondence to Maria Maximova .

Editor information

Editors and Affiliations

  1. Universidad Autónoma de Madrid, Madrid, Spain

    Juan de Lara

  2. University of York, York, United Kingdom

    Detlef Plump

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Maximova, M., Giese, H., Krause, C. (2017). Probabilistic Timed Graph Transformation Systems. In: de Lara, J., Plump, D. (eds) Graph Transformation. ICGT 2017. Lecture Notes in Computer Science(), vol 10373. Springer, Cham. https://doi.org/10.1007/978-3-319-61470-0_10

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  • DOI: https://doi.org/10.1007/978-3-319-61470-0_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61469-4

  • Online ISBN: 978-3-319-61470-0

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