Abstract
This paper introduces an extension of the Generalized Stochastic Petri Net (GSPN) formalism in order to enable the computation of first passage time distributions of tokens. A “tagged token” technique is used which relies on net’s structural properties to guide the correct specification of this extension. The extended model is suited for an automatic translation into an ordinary GSPN that can be used for the first passage time analysis. Scheduling policies of tokens in places, that are neglected in ordinary GSPNs, become relevant in the Tagged Generalized Stochastic Petri Net (TGSPN) formalism and specific submodels are proposed which are then used during the translation from TGSPNs to ordinary GSPNs. A running example inspired by a Flexible Manufacturing application is used throughout the paper to introduce the different concepts and to provide evidence of the relevance of the results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. J. Wiley, Chichester (1995)
Balbo, G., De Pierro, M., Franceschinis, G.: Tagged generalized stochastic Petri nets. Technical Report (2009), http://www.di.unito.it/~depierro/articoli.html
Bause, F., Buchholz, P., Kemper, P.: Hierarchically combined Queueing Petri Nets. In: Proc. 11th Int. Conf. on Analysis and Optimization of Systems, Discrete Event Systems, Sophia-Antipolis, pp. 176–182 (1994)
Bause, F., Kemper, P.: QPN-tool for qualitative and quantitative analysis of Queueing Petri Nets. In: Haring, G., Kotsis, G. (eds.) TOOLS 1994. LNCS, vol. 794, pp. 321–334. Springer, Heidelberg (1994)
Bodrog, L., Horvath, G., Racz, S., Telek, M.: A tool support for automatic analysis based on the tagged customer approach. In: Proc. of the 3rd int. conf. on the Quantitative Evaluation of Systems 2006, Washington, DC, USA, pp. 323–332. IEEE, Los Alamitos (2006)
Bradley, J.T., Dingle, N.J., Knottenbelt, W.J., Wilson, H.J.: Hypergraph-based parallel computation of passage time densities in large semi-Markov models. Journal of Linear Algebra and its Applications 386, 311–334 (2004)
Dingle, N.J., Knottenbelt, W.J.: Automated Customer-Centric Performance Analysis of Generalised Stochastic Petri Nets Using Tagged Tokens. In: Proc. of the 3rd Int. Workshop on Practical Applications of Stochastic Modelling (PASM 2008) (September 2008)
Kounev, S., Dutz, C., Buchmann, A.: QPME – Queueing Petri Net Modeling Environment. In: QEST 2006: Proceedings of the 3rd international conference QEST 2006, Washington, DC, USA, pp. 115–116. IEEE CS, Los Alamitos (2006)
Kulkarni, V.G.: Modeling and Analysis of Stochastic Systems. Chapman & Hall, London (1995)
Miner, A.S.: Computing response time distributions using stochastic Petri nets and matrix diagrams. In: Petri Nets and Performance Models 2003, p. 10. IEEE, Los Alamitos (2003)
Nelson, R.: Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Evaluation. Springer, Heidelberg (1995)
Suto, T., Bradley, J.T., Knottenbelt, W.J.: Performance trees: Expressiveness and quantitative semantics. In: Proc. of the 4th International Conference on Quantitative Evaluation of Systems (QEST 2007), Edinburgh, UK. IEEE, Los Alamitos (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Balbo, G., De Pierro, M., Franceschinis, G. (2009). Tagged Generalized Stochastic Petri Nets. In: Bradley, J.T. (eds) Computer Performance Engineering. EPEW 2009. Lecture Notes in Computer Science, vol 5652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02924-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-02924-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02923-3
Online ISBN: 978-3-642-02924-0
eBook Packages: Computer ScienceComputer Science (R0)