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Erschienen in:
The Pullback-Pushout Approach to Algebraic Graph Transformation Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Probabilistic Timed Graph Transformation Systems

verfasst von : Maria Maximova, Holger Giese, Christian Krause

Erschienen in: Graph Transformation

Verlag: Springer International Publishing

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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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Vorheriges Kapitel k-Inductive Invariant Checking for Graph Transformation Systems
Nächstes Kapitel Leveraging Incremental Pattern Matching Techniques for Model Synchronisation
Fußnoten
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
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
For an arbitrary set M, \(2_{\mathrm {fn}}^{M} \) denotes the set of finite nonempty subsets of M.
 
4
\( rhs (\rho )\) denotes the right-hand side of the rule \(\rho \).
 
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
For morphisms between clocks we omit the restricted notation https://static-content.springer.com/image/chp%3A10.1007%2F978-3-319-61470-0_10/453698_1_En_10_IEq199_HTML.gif and use the unrestricted notation https://static-content.springer.com/image/chp%3A10.1007%2F978-3-319-61470-0_10/453698_1_En_10_IEq200_HTML.gif to simplify the representation.
 
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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Metadaten
Titel
Probabilistic Timed Graph Transformation Systems
verfasst von
Maria Maximova
Holger Giese
Christian Krause
Copyright-Jahr
2017
Buch
Graph Transformation

Print ISBN: 978-3-319-61469-4

Electronic ISBN: 978-3-319-61470-0

Copyright-Jahr: 2017

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

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