Summary
A general iterative technique for approximate throughput computation of stochastic strongly connected marked graphs is presented. It generalizes a previous technique based on net decomposition through a single input-single output cut, allowing the split of the model through any cut. The approach has two basic foundations. First, a deep understanding of the qualitative behaviour of marked graphs leads to a general decomposition technique. Second, after the decomposition phase, an iterative response time approximation method is applied for the computation of the throughput. Experimental results on several examples generally have an error of less than 3%. The state space is usually reduced by more than one order of magnitude; therefore the analysis of otherwise intractable systems is possible.
This work was partially supported by the European ESPRIT BRA Project 7269 QMIPS, the Spanish PRONTIC’s 354/91 and 242/94, and the Aragonese CONAI-DGA P-IT 6/91.
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S.C. Agrawal, J.P. Buzen, and A.W. Shum, “Response time preservation: A general technique for developing approximate algorithms for queueing networks”, In Proc. of the 1984 ACM Sigmetrics Conf. on Measurement and Modeling of Computer Systems, pp. 63-77, Cambridge, MA, Aug. 1984.
A.V. Aho, J.E. Hopcroft, and J.D. Ullman, Data Structures and Algorithms, Addison-Wesley, 1983.
M. Ajmone Marsan, G. Balbo, and G. Conte, Performance Models of Multiprocessor Systems. MIT Press, Cambridge, 1986.
H.H. Ammar and S.M.R. Islam, “Time scale decomposition of a class of generalized stochastic Petri net models”, IEEE Trans. Software Eng., 15(6), pp. 809–820, June 1989.
F. Baccelli and Z. Liu, “Comparison properties of stochastic decision free Petri nets”, IEEE Trans. Automat. Contr., 37(12), pp. 1905–1920, Dec. 1992.
B. Baynat and Y. Dallery, “Approximate techniques for general closed queueing networks with subnetworks having population constraints”, European Journal of Operational Research, 69 pp. 250–263, 1993.
B. Baynat and Y. Dallery, “A unified view of product-form approximation techniques for general closed queueing networks”, Performance Evaluation, 18(3), pp. 205–224, Nov. 1993.
J. Campos, G. Chiola, J. M. Colom, and M. Silva, “Properties and performance bounds for timed marked graphs”, IEEE Trans. Circuits and Syst.—I: Fundamental Theory and Applications, 39(5), pp. 386–401, May 1992.
J. Campos, J. M. Colom, H. Jungnitz, and M. Silva, “Approximate throughput computation of stochastic marked graphs”, IEEE Trans. Software Eng., 20(7), pp. 526–535, July 1994.
G. Chiola, “A graphical Petri net tool for performance analysis”, In Proc. of the 3rd Int. Workshop on Modeling Techniques and Performance Evaluation, Paris, France, March 1987. AFCET.
G. Ciardo and K. Trivedi, “A decomposition approach for stochastic Petri nets models”, In Proc. of the 4th Int. Workshop on Petri Nets and Performance Models, pp. 74-83, Melbourne, Australia, Dec. 1991. IEEE Comput. Soc. Press.
J.M. Colom, Análisis Estructural de Redes de Petri, Programadón Lineal y Geometría Convexa, PhD thesis, Dpto. de Ingeniería Eléctrica e Informática, Univ. Zaragoza, Spain, June 1989.
J.M. Colom and M. Silva, “Improving the linearly based characterization of P/T nets”, In G. Rozenberg (ed.), Advances in Petri Nets 1990, 483 of LNCS, pp. 113–145. Springer-Verlag, Berlin, 1991.
Y. Dallery, Z. Liu, and D. Towsley, “Equivalence, reversibility, symmetry, and concavity properties in fork-join queueing networks with blocking”, Journal of the ACM, 41(5), pp. 903–942, Sep. 1994.
A. Desrochers, H. Jungnitz, and M. Silva, “An approximation method for the performance analysis of manufacturing systems based on GSPN’s”, In Proc. of the Rensselaer’s Third Int. Conf. on Computer Integrated Manufacturing, pp. 46-55, Troy, NY, May 1992, IEEE Comput. Soc. Press.
S. Donatelli and M. Sereno, “On the product form solution for stochastic Petri nets”, In Proc. of the 13th Int. Conf. on Applications and Theory of Petri Nets, pp. 154-172, Sheffield, UK, June 1992.
H. Jungnitz, B. Sánchez, and M. Silva, “Approximate throughput computation of stochastic marked graphs”, Journal of Parallel and Distributed Computing, 15, pp. 282–295, 1992.
H.J. Jungnitz, Approximation Methods for Stochastic Petri Nets. PhD thesis, Dept. of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY, May 1992.
Y. Li and C.M. Woodside, “Iterative decomposition and aggregation of stochastic marked graphs Petri nets”, In Proc. of the 12th Int. Conf. on Applications and Theory of Petri Nets, pp. 257-275, Gjern, Denmark, June 1991.
Y. Li and C.M. Woodside, “Performance Petri net analysis of communications protocol software by delay-equivalent aggregation”, In Proc. of the 4th Int. Workshop on Petri Nets and Performance Models, pp. 64-73, Melbourne, Australia, Dec. 1991, IEEE Comput. Soc. Press.
R.A. Marie, “An approximate analytical method for general queueing networks”, IEEE Trans. Software Eng., 5(5), pp. 530–538, Sep. 1979.
T. Murata, “Petri nets: Properties, analysis, and applications”, Proceedings of the IEEE, 77(4), pp. 541–580, April 1989.
M. Silva, Las Redes de Petri en la Automática y la Informática. Editorial AC, Madrid, 1985.
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Campos, J., Colom, J.M., Jungnitz, H., Silva, M. (1995). Approximate Throughput Computation of Stochastic Marked Graphs. In: Baccelli, F., Jean-Marie, A., Mitrani, I. (eds) Quantitative Methods in Parallel Systems. Esprit Basic Research Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79917-4_12
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DOI: https://doi.org/10.1007/978-3-642-79917-4_12
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