Numerical Results for the Automated Rare Event Simulation of Stochastic Petri Nets

Model-based evaluation of highly reliable dynamic systems is an important help in their design. Rare-event simulation techniques are necessary to avoid unacceptably long simulation run times. Their application usually requires human insight for a proper configuration. However, it is possible to derive the necessary information from high-level model descriptions such as stochastic Petri nets. This paper presents numerical results for two implemented algorithms that have been proposed in this area, one based on importance sampling, and the other on RESTART splitting. A comparison of the methods discusses advantages and disadvantages.

[1]  C. Kelling,et al.  Rare event simulation with an adaptive "RESTART" method in a Petri net modeling environment , 1996, Proceedings of the 4th International Workshop on Parallel and Distributed Real-Time Systems.

[2]  Jan-Kees C. W. van Ommeren,et al.  On the importance function in splitting simulation , 2002, Eur. Trans. Telecommun..

[3]  Marco Ajmone Marsan,et al.  Modelling with Generalized Stochastic Petri Nets , 1995, PERV.

[4]  Daniël Reijsbergen,et al.  Efficient simulation techniques for stochastic model checking , 2013 .

[5]  Manuel Villén-Altamirano,et al.  Enhancement of the Accelerated Simulation Method RESTART by Considering Multiple Thresholds , 1994 .

[6]  Paul Glasserman,et al.  Multilevel Splitting for Estimating Rare Event Probabilities , 1999, Oper. Res..

[7]  Cyrille Jégourel,et al.  A Platform for High Performance Statistical Model Checking - PLASMA , 2012, TACAS.

[8]  Manuel Silva Suárez,et al.  Structural techniques and performance bounds of stochastic Petri net models , 1992, Advances in Petri Nets: The DEMON Project.

[9]  Bruno Tuffin,et al.  Approximate zero-variance simulation , 2008, 2008 Winter Simulation Conference.

[10]  Dirk P. Kroese,et al.  A comparison of RESTART implementations , 1998, 1998 Winter Simulation Conference. Proceedings (Cat. No.98CH36274).

[11]  Gianfranco Ciardo,et al.  Using Edge-Valued Decision Diagrams for Symbolic Generation of Shortest Paths , 2002, FMCAD.

[12]  Günter Hommel,et al.  TimeNET: A Toolkit for Evaluating Non-Markovian Stochastic Petri Nets , 1995, Perform. Evaluation.

[13]  Armin Zimmermann.  Dependability evaluation of complex systems with TimeNET , 2010 .

[14]  José Villén-Altamirano,et al.  Analysis of restart simulation: Theoretical basis and sensitivity study , 2002, Eur. Trans. Telecommun..

[15]  Armin Zimmermann.  Importance Function Derivation for RESTART Simulations of Petri Nets , 2012 .

[16]  Armin Zimmermann,et al.  Stochastic Discrete Event Systems , 2008 .

[17]  Peter J. Haas,et al.  Stochastic Petri Nets: Modelling, Stability, Simulation , 2002 .

[18]  Reinhard German,et al.  Performance analysis of communication systems - modelling with non-Markovian stochastic Petri nets , 2000, Wiley-Interscience series in systems and optimization.

[19]  Philip Heidelberger,et al.  Fast simulation of rare events in queueing and reliability models , 1993, TOMC.

[20]  Armin Zimmermann.  Modeling and evaluation of stochastic Petri nets with TimeNET 4.1 , 2012, 6th International ICST Conference on Performance Evaluation Methodologies and Tools.

[21]  José Villén-Altamirano,et al.  RESTART: a straightforward method for fast simulation of rare events , 1994, Proceedings of Winter Simulation Conference.

[22]  William H. Sanders,et al.  An environment for importance sampling based on stochastic activity networks , 1994, Proceedings of IEEE 13th Symposium on Reliable Distributed Systems.

[23]  Gianfranco Ciardo,et al.  A Characterization of the Stochastic Process Underlying a Stochastic Petri Net , 1994, IEEE Trans. Software Eng..

[24]  Kishor S. Trivedi,et al.  Implementation of Importance Splitting Techniques in Stochastic Petri Net Package , 2000, Computer Performance Evaluation / TOOLS.

[25]  Günter Hommel,et al.  Towards modeling and evaluation of ETCS real-time communication and operation , 2005, Journal of Systems and Software.

[26]  Armin Zimmermann,et al.  RESTART Simulation of Colored Stochastic Petri Nets , 2008 .

[27]  Stefan Edelkamp,et al.  Action Planning for Directed Model Checking of Petri Nets , 2006, MoChArt@CONCUR/SPIN.

[28]  Boudewijn R. Haverkort,et al.  Automated Rare Event Simulation for Stochastic Petri Nets , 2013, QEST.

[29]  Kishor S. Trivedi,et al.  Dependability modeling using Petri-nets , 1995 .

[30]  Christian Kelling.  A framework for rare event simulation of stochastic Petri nets using “RESTART” , 1996, Winter Simulation Conference.

[31]  Philip Heidelberger,et al.  Modeling and analysis of system dependability using the System Availability Estimator , 1994, Proceedings of IEEE 24th International Symposium on Fault- Tolerant Computing.

[32]  Manuel Silva Suárez,et al.  Linear Algebraic and Linear Programming Techniques for the Analysis of Place or Transition Net Systems , 1996, Petri Nets.