Abstract
In concurrent real-time processes, the speed of individual components has a double impact: on the one hand, the overall latency of a compound process is affected by the latency of its components. But, if the composition has race conditions, the very outcome of the process will also depend on the latency of component processes. Using stochastic Petri nets, we investigate the probability of a transition occurrence being critical for the entire process, i.e. such that a small increase or decrease of the duration of the occurrence entails an increase or decrease of the total duration of the process. The first stage of the analysis focuses on occurrence nets, as obtained by partial order unfoldings, to determine criticality of events; we then lift to workflow nets to investigate criticality of transitions inside a workflow.
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References
van der Aalst, W.M.P.: The application of Petri Nets to Workflow Management. Journal of Circuits, Systems and Computers 8(1), 21–66 (1998)
van der Aalst, W.M.P.: Verification of Workflow nets. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 407–426. Springer, Heidelberg (1997)
Abbes, S., Benveniste, A.: True-concurrency probabilistic models: Markov nets and a law of large numbers. Theor. Comput. Sci. 390(2-3), 129–170 (2008)
Abbes, S., Benveniste, A.: Probabilistic models for true-concurrency: branching cells and distributed probabilities for event structures. Information and Computation 204(2), 231–274 (2006)
Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modeling with Generalized Stochastic Petri Nets. Parallel Computing Series. Wiley, Chichester (1995)
Benveniste, A., Fabre, E., Haar, S.: Markov Nets: Probabilistic Models for distributed and concurrent systems. IEEE Trans. Aut. Control 48(11), 1936–1950 (2003)
Bouillard, A., Haar, S., Rosario, S.: Critical paths in the Partial Order Unfolding of a Stochastic Petri Net. INRIA Research report (August 2009)
Bouillard, A., Rosario, S., Benveniste, A., Haar, S.: Monotonicity in Service Orchestrations. Petri Nets (2009), http://petrinets2009.lip6.fr/
Engelfriet, J.: Branching Processes of Petri Nets. Acta Informatica 28, 575–591 (1991)
Esparza, J., Römer, S., Vogler, W.: An improvement of McMillan’s unfolding algorithm. Formal Methods in System Design 20(3), 285–310 (2002)
Haas, P.: Stochastic Petri Nets. Modelling, Stability, Simulation. Springer Series in Operations Research, Berlin (2002)
Katoen, J.-P., Baier, C., Latella, D.: Metric semantics for true concurrent real time. Theoretical Computer Science 254, 501–542 (2001)
Mairesse, J., Gaubert, S.: Modeling and Analysis of Timed Petri Nets using Heaps of Pieces. IEEE Trans. Autom. Control 44(4), 683–697 (1999)
McMillan, K.: Using Unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. In: 4th Workshop on Computer Aided Verification, pp. 164–174 (1992)
Nielsen, M., Plotkin, G., Winskel, G.: Petri nets, event structures, and domains, Part I. TCS 13, 85–108 (1981)
Ruys, T.C., Langerak, R., Katoen, J.-P., Latella, D., Massink, M.: First passage time analysis of stochastic process algebra using partial orders. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 220–235. Springer, Heidelberg (2001)
Rosario, S., Benveniste, A., Haar, S., Jard, C.: Probabilistic QoS and soft contracts for transaction based Web services. In: Proceedings ICWS 2007, pp. 126–133 (2007)
Rosario, S., Kitchin, D.E., Benveniste, A., Cook, W., Haar, S., Jard, C.: Event structure semantics of orc. In: Dumas, M., Heckel, R. (eds.) WS-FM 2007. LNCS, vol. 4937, pp. 154–168. Springer, Heidelberg (2008); long version as INRIA Research Report Nr 6221
Tucker, H.G.: An Introduction to probability and mathematical statistics. Academic Press, London (1962)
Varacca, D., Völzer, H., Winskel, G.: Probabilistic event structures and domains. Theor. Comput. Sci. 358(2-3), 173–199 (2006)
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Bouillard, A., Haar, S., Rosario, S. (2009). Critical Paths in the Partial Order Unfolding of a Stochastic Petri Net. In: Ouaknine, J., Vaandrager, F.W. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2009. Lecture Notes in Computer Science, vol 5813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04368-0_6
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DOI: https://doi.org/10.1007/978-3-642-04368-0_6
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