Abstract
This paper descibes the transient analysis component for deterministic and stochastic Petri nets which has recently been added to the software package TimeNET. The technique is based on the derivation of state equations by the method of supplementary variables. The system of equations consists of partial and ordinary differential equations which are combined with initial and boundary conditions. Algorithms for the numerical analysis of the equations are presented. Emphasis is put on implementation aspects. Different cases are identified for which different variants of the algorithms can be used. The computational complexity is investigated by asymptotical expressions and by measurements. Several examples are used in order to illustrate the modeling process and transient analysis with TimeNET.
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References
M. Ajmone Marsan, G. Chiola. On Petri Nets with Deterministic and Exponentially Distributed Firing Times. Advances in Petri Nets 1986, Lecture Notes in Computer Science 266, pp. 132–145, Springer 1987.
A. Bobbio, M. Telek. Markov Regenerative SPN with Non-Overlapping Activity Cycles. Proc. IEEE Int. Performance and Dependability Symp., Erlangen, Germany, pp. 124–133, 1995.
G. Chiola. GreatSPN 1.5 Software Architecture. Proc. 5th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, Torino, Italy, pp. 117–132, 1991.
H. Choi, V. G. Kulkarni, K. S. Trivedi. Transient Analysis of Deterministic and Stochastic Petri Nets. Proc. 14th Int. Conf. on Application and Theory of Petri Nets, Chicago, IL, USA, pp. 166–185, 1993.
B. L. Fox, P. W. Glynn. Computing Poisson Probabilities. Comm. of the ACM, 31 (1988) 440–445.
G. Ciardo, J. Muppala, K. S. Trivedi. SPNP: Stochastic Petri Net Package. Proc. 3rd Int. Workshop on Petri Nets and Performance Models, Kyoto, Japan, pp. 142–151, 1989.
D.R. Cox. The Analysis of Non-Markov Stochastic Processes by the Inclusion of Supplementary Variables. Proc. Camb. Phil. Soc. (Math. and Phys. Sciences), 51 (1955) 433–441.
R. German. New Results for the Analysis of Deterministic and Stochastic Petri Nets. Proc. IEEE Int. Performance and Dependability Symp., Erlangen, Germany, pp. 114–123, 1995.
R. German, C. Kelling, A. Zimmermann, G. Hommel. TimeNET: A Toolkit for Evaluating Non-Markovian Stochastic Petri Nets. Perf. Eval. (to appear).
R. German, C. Lindemann. Analysis of Stochastic Petri Nets by the Method of Supplementary Variables. Perf. Eval., 20 (1994) 317–335.
R. German, D. Logothetis, K. S. Trivedi. Transient Analysis of Markov Regenerative Stochastic Petri Nets: A Comparison of Approaches. Proc. 6th Int. Workshop on Petri Nets and Performance Models, Durham, NC, USA, 1995 (to appear).
D. Gross, D.R. Miller. The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes. Operations Research, 32 (1984) 345–361.
C. Lindemann. DSPNexpress: A Software Package for the Efficient Solution of Deterministic and Stochastic Petri Nets. Perf. Eval., (to appear).
D. Logothetis, K. S. Trivedi. Transient Analysis of the Leaky Bucket Rate Control Scheme Under Poisson and ON-OFF Sources. Proc. of INFOCOM '94, Toronto, Canada, 1994.
D. Logothetis, K.S. Trivedi. Time-Dependent Behavior of Redundant Systems with Deterministic Repair. 2nd Int. Workshop Numerical Solution of Markov Chains, Raleigh, NC, USA, 1995.
D. Logothetis, K. S. Trivedi, A. Puliafito. Markov Regenerative Models. Proc. IEEE Int. Computer Performance and Dependability Symp., Erlangen, Germany, pp. 134–142, 1995.
M. Lu, D. Zhang, T. Murata. Analysis of Self-Stabilizing Clock Synchronization by Means of Stochastic Petri Nets. IEEE Trans. on Comp., 39 (1990) 597–604.
W. H. Sanders, W. D. Obal II, M. A. Qureshi, F. K. Widjanarko. The UltraSAN Modeling Environment. Perf. Eval., (to appear).
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© 1995 Springer-Verlag Berlin Heidelberg
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German, R., Mitzlaff, J. (1995). Transient analysis of deterministic and stochastic Petri nets with TimeNET. In: Beilner, H., Bause, F. (eds) Quantitative Evaluation of Computing and Communication Systems. TOOLS 1995. Lecture Notes in Computer Science, vol 977. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024317
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DOI: https://doi.org/10.1007/BFb0024317
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