Abstract
Graph transformation systems (GTS) have been proposed for high-level stochastic modelling of dynamic systems and networks. The resulting systems can be described as semi-Markov processes with graphs as states and transformations as transitions. The operational semantics of such processes can be explored through stochastic simulation. In this paper, we develop the basic theory of stochastic graph transformation, including generalisations of the Parallelism and Concurrency Theorems and their application to computing the completion time of a concurrent process.
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References
Brandt, C., Hermann, F., Groote, J.F.: Generation and Evaluation of Business Continuity Processes; Using Algebraic Graph Transformation and the mCRL2 Process Algebra. Journal of Research and Practice in Information Technology 43(1), 65–85 (2011)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Monographs in Theoretical Computer Science. An EATCS Series. Springer-Verlag New York, Inc., Secaucus (2006)
Grinstead, C., Snell, J.: Introduction to Probability. Dartmouth Chance Project (2005), http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
Heckel, R.: Stochastic Analysis of Graph Transformation Systems: A Case Study in P2P Networks. In: Van Hung, D., Wirsing, M. (eds.) ICTAC 2005. LNCS, vol. 3722, pp. 53–69. Springer, Heidelberg (2005)
Hermann, F.: Analysis and Optimization of Visual Enterprise Models Based on Graph and Model Transformation. Ph.D. thesis, TU Berlin (2011), http://opus.kobv.de/tuberlin/volltexte/2011/3008/
Lack, S., Sobociński, P.: Adhesive Categories. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 273–288. Springer, Heidelberg (2004)
van der Linden, W.J.: A lognormal model for response times on test items. Journal of Educational and Behavioral Statistics 31(2), 181–204 (2006)
Wolfram Research: Mathematica 8.0 (2012), http://www.wolfram.com/
Mielke, A.: Elements for response-time statistics in ERP transaction systems. Perform. Eval. 63(7), 635–653 (2006)
Möhring, R.H.: Scheduling under Uncertainty: Bounding the Makespan Distribution. In: Alt, H. (ed.) Computational Discrete Mathematics. LNCS, vol. 2122, pp. 79–97. Springer, Heidelberg (2001)
TFS, TU Berlin: AGG: The Attributed Graph Grammar System, http://tfs.cs.tu-berlin.de/agg/
Torrini, P., Heckel, R., Ráth, I.: Stochastic Simulation of Graph Transformation Systems. In: Rosenblum, D.S., Taentzer, G. (eds.) FASE 2010. LNCS, vol. 6013, pp. 154–157. Springer, Heidelberg (2010)
Varró, D., Balogh, A.: The model transformation language of the VIATRA2 framework. Sci. Comput. Program. 68(3), 214–234 (2007)
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Heckel, R., Ehrig, H., Golas, U., Hermann, F. (2012). Parallelism and Concurrency of Stochastic Graph Transformations. In: Ehrig, H., Engels, G., Kreowski, HJ., Rozenberg, G. (eds) Graph Transformations. ICGT 2012. Lecture Notes in Computer Science, vol 7562. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33654-6_7
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DOI: https://doi.org/10.1007/978-3-642-33654-6_7
Publisher Name: Springer, Berlin, Heidelberg
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