On the fluidization of Petri nets and marking homothecy

Abstract The analysis of Discrete Event Dynamic Systems suffers from the well known state explosion problem . A classical technique to overcome it is to relax the behavior by partially removing the integrality constraints and thus to deal with hybrid or continuous systems. In the Petri nets framework, continuous net systems (technically hybrid systems) are the result of removing the integrality constraint in the firing of transitions. This relaxation may highly reduce the complexity of analysis techniques but may not preserve important properties of the original system. This paper deals with the basic operation of fluidization. More precisely, it aims at establishing conditions that a discrete system must satisfy so that a given property is preserved by the continuous relaxation. These conditions will be mainly based on the marking homothetic behavior of the system. The focus will be on logical properties as boundedness, B-fairness, deadlock-freeness, liveness and reversibility. Furthermore, testing homothetic monotonicity of some properties in the discrete systems is also studied, as well as techniques to improve the quality of the fluid relaxation by removing spurious solutions.

[1]  Manuel Silva Suárez,et al.  On the Computation of Structural Synchronic Invariants in P/T Nets , 1988, European Workshop on Applications and Theory of Petri Nets.

[2]  Fernando García Vallés Contributions to the structural and symbolic analysis of place/transition nets, with applications to flexible manufacturing systems and asynchronous circuits , 1999 .

[3]  Manuel Silva Suárez,et al.  Autonomous Continuous P/T Systems , 1999, ICATPN.

[4]  Giovanni Chiola,et al.  Ergodicity and Throughput Bounds of Petri Nets with Unique Consistent Firing Count Vector , 1991, IEEE Trans. Software Eng..

[5]  Li Jiao,et al.  Characterizing Liveness Monotonicity for Weighted Petri Nets in Terms of Siphon-Based Properties , 2003, Int. J. Found. Comput. Sci..

[6]  Simon Peck,et al.  Practice of Petri Nets in Manufacturing , 1993 .

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

[8]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[9]  Javier Martínez,et al.  A Petri net based deadlock prevention policy for flexible manufacturing systems , 1995, IEEE Trans. Robotics Autom..

[10]  Cristian Mahulea,et al.  Basic Server Semantics and Performance Monotonicity of Continuous Petri Nets , 2009, Discret. Event Dyn. Syst..

[11]  Olivia Oanea,et al.  New Algorithms for Deciding the Siphon-Trap Property , 2010, Petri Nets.

[12]  Hassane Alla,et al.  Discrete, continuous, and hybrid Petri Nets , 2004 .

[13]  Cristian Mahulea,et al.  On fluidization of discrete event models: observation and control of continuous Petri nets , 2011, Discret. Event Dyn. Syst..

[14]  Manuel Silva Suárez,et al.  Structure Theory of Equal Conflict Systems , 1996, Theor. Comput. Sci..

[15]  Manuel Silva Suárez,et al.  Structure theory of multi-level deterministically synchronized sequential processes , 2001, Theor. Comput. Sci..

[16]  Tadao Murata,et al.  B-Fairness and Structural B-Fairness in Petri Net Models of Concurrent Systems , 1992, J. Comput. Syst. Sci..

[17]  Manuel Silva Suárez,et al.  Petri nets and integrality relaxations: A view of continuous Petri net models , 2002, IEEE Trans. Syst. Man Cybern. Part C.