Backward Coupling in Bounded Free-Choice Nets Under Markovian and Non-Markovian Assumptions
- 58 Downloads
In this paper, we show how to design a perfect sampling algorithm for stochastic Free-Choice Petri nets by backward coupling. For Markovian event graphs, the simulation time can be greatly reduced by using extremal initial states, namely blocking marking, although such nets do not exhibit any natural monotonicity property. Another approach for perfect simulation of non-Markovian event graphs is based on a (max,plus) representation of the system and the theory of (max,plus) stochastic systems. We also show how to extend this approach to one-bounded free choice nets to the expense of keeping all states. Finally, experimental runs show that the (max,plus) approach needs a larger simulation time than the Markovian approach.
KeywordsPetri nets Perfect simulation Heaps of pieces Max-plus systems
The authors would like to thank Jean Mairesse for his precious advices.
- Baccelli F, Foss S, Mairesse J (1996) Stationary ergodic jackson networks: results and counter-examples. Stochastic networks, Oxford Univ. Press, pp 281–307Google Scholar
- Baccelli F, Gohen G, Olsder G, Quadrat, J-P (1992) Synchronization and linearity. WileyGoogle Scholar
- Baccelli F, Jean-Marie A, Mitrani I (eds) (1995) Quantitative methods in parallel systems. Basic Research Series. SpringerGoogle Scholar
- Baccelli F, Mairesse J (1998) Idempotency. Chapter ergodic theory of stochastic operators and discrete event networks. Publications of the Isaac Newton Institute. Cambridge Univ. Press, pp 171–208Google Scholar
- Bouillard A, Gaujal B (2001) Coupling time of a (max,plus) matrix. In: Workshop on Max-Plus algebras and their applications to discrete-event systems. Theoretical Computer Science, and Optimization, Prague. IFACGoogle Scholar
- Bouillard A, Gaujal B (2006) Backward coupling in petri nets. In: Valuetools, Pisa, ItalyGoogle Scholar
- Desel J, Esparza J (1995) Free choice Petri nets. Cambridge Tracts in Theorical Computer ScienceGoogle Scholar
- Häggström O (2002) Finite Markov chains and Algorithmic Applications, vol 52 of Student texts. Cambridge Univ. PressGoogle Scholar
- Walker A (1974) An efficient method for generating random variables with general distributions. ACM Trans Math Softw 253–256Google Scholar