Abstract
Passage time measures specification and computation for Generalized Stochastic Petri Net models have been faced in the literature from different points of view. In particular three aspects have been developed: (1) how to select a specific token (called the tagged token) and measure the distribution of the time employed from an entry to an exit point in a subnet; (2) how to specify in a flexible way any condition on the paths of interest to be measured, (3) how to efficiently compute the required distribution. In this paper we focus on the last two points: the specification and computation of complex passage time measures in (Tagged) GSPNs using the Hybrid Automata Stochastic Logic (HASL) and the statistical model checker COSMOS. By considering GSPN models of two different systems (a flexible manufacturing system and a workflow), we identify a number of relevant performance measures (mainly passage-time distributions), formally express them in HASL terms and assess them by means of simulation in the COSMOS tool. The interest from the measures specification point of view is provided by the possibility of setting one or more timers along the paths, and setting the conditions for the paths selection, based on the measured values of such timers. With respect to other specification languages allowing to use timers in the specification of performance measures, HASL provides timers suspension, reactivation, and rate change along a path.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
van der Aalst, W.M.P.: Business process management demystified: A tutorial on models, systems and standards for workflow management. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) ACPN 2003, LNCS, vol. 3098, pp. 1–65. Springer, Heidelberg (2004), http://dx.doi.org/10.1007/978-3-540-27755-2_1
Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.H.: Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) HS 1991 and HS 1992. LNCS, vol. 736, pp. 209–229. Springer, Heidelberg (1993)
Amparore, E., Beccuti, M., Donatelli, S., Franceschinis, G.: Probe automata for passage time specification. In: Quantitative 2011 Eighth International Conference on Evaluation of Systems (QEST), pp. 101–110 (September 2011)
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model-checking continuous-time Markov chains. ACM Trans. Comput. Logic 1(1), 162–170 (2000)
Baier, C., Cloth, L., Haverkort, B.R., Kuntz, M., Siegle, M.: Model Checking Markov Chains with Actions and State Labels. IEEE Transactions on Software Engineering 33, 209–224 (2007)
Balbo, G., Beccuti, M., De Pierro, M., Franceschinis, G.: First Passage Time Computation in Tagged GSPNs with Queue Places. The Computer Journal (2010) (first published online July 22, 2010)
Balbo, G., De Pierro, M., Franceschinis, G.: Tagged Generalized Stochastic Petri Nets. In: Bradley, J.T. (ed.) EPEW 2009. LNCS, vol. 5652, pp. 1–15. Springer, Heidelberg (2009)
Ballarini, P., Djafri, H., Duflot, M., Haddad, S., Pekergin, N.: COSMOS: a statistical model checker for the hybrid automata stochastic logic. In: Proceedings of the 8th International Conference on Quantitative Evaluation of Systems (QEST 2011), pp. 143–144. IEEE Computer Society Press (September 2011)
Ballarini, P., Djafri, H., Duflot, M., Haddad, S., Pekergin, N.: HASL: an expressive language for statistical verification of stochastic models. In: Proc. Valuetools (2011)
Chen, T., Han, T., Katoen, J.P., Mereacre, A.: Quantitative Model Checking of Continuous-Time Markov Chains Against Timed Automata Specifications. In: Symposium on Logic in Computer Science, pp. 309–318 (2009)
Clark, A., Gilmore, S.: State-aware performance analysis with extended stochastic probes. In: Thomas, N., Juiz, C. (eds.) EPEW 2008. LNCS, vol. 5261, pp. 125–140. Springer, Heidelberg (2008), http://dx.doi.org/10.1007/978-3-540-87412-6_10
Dingle, N.J., Knottenbelt, W.J.: Automated Customer-Centric Performance Analysis of Generalised Stochastic Petri Nets Using Tagged Tokens. Electron. Notes Theor. Comput. Sci. 232, 75–88 (2009)
Dingle, N.J., Harrison, P.G., Knottenbelt, W.J.: Uniformisation and Hypergraph Partitioning for the Distributed Computation of Response Time Densities in Very Large Markov Models. Journal of Parallel and Distributed Computing 64(8), 309–920 (2004)
Djafri, H.: Numerical and Statistical Approaches for Model Checking of Stochastic Processes. Ph.D. thesis, ENS Cachan (June 2012)
Donatelli, S., Haddad, S., Sproston, J.: Model checking timed and stochastic properties with CSLTA. IEEE Trans. Softw. Eng. 35(2), 224–240 (2009)
Haverkort, B., Cloth, L., Hermanns, H., Katoen, J.P., Baier, C.: Model checking performability properties. In: Proc. DSN 2002 (2002)
Hillston, J.: Process algebras for quantitative analysis. In: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science, pp. 239–248. IEEE Computer Society, Washington, DC (2005), http://portal.acm.org/citation.cfm?id=1078035.1079698
Kulkarni, V.: Modeling and Analysis of Stochastic Systems. Chapman & Hall, London (1995)
Obal II, W.D., Sanders, W.H.: State-space support for path-based reward variables. Perform. Eval. 35, 233–251 (1999), http://dx.doi.org/10.1016/S0166-53169900010-3
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Amparore, E.G., Ballarini, P., Beccuti, M., Donatelli, S., Franceschinis, G. (2013). Expressing and Computing Passage Time Measures of GSPN Models with HASL. In: Colom, JM., Desel, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2013. Lecture Notes in Computer Science, vol 7927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38697-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-38697-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38696-1
Online ISBN: 978-3-642-38697-8
eBook Packages: Computer ScienceComputer Science (R0)