#### DMCA

## Modeling and Analysis of Timed Petri Nets Using Heaps of Pieces (1997)

### Cached

### Download Links

Citations: | 56 - 18 self |

### Citations

2135 | Petri nets: Properties, analysis and applications,” - Murata - 1989 |

965 | Petri net theory and the modeling of systems - Peterson - 1981 |

366 |
Scheduling Algorithms
- Brucker
- 2007
(Show Context)
Citation Context ...d w = abcd. Piece c is an example of a non connected (but \rigid") piece. b b a c d a c d Fig. 1. Heap of pieces associated with the word w = abcd. We can read directly on Fig. 1 the values x H (w) = =-=[4; 6; 8; 6]-=- and y H (w) = 8. Denition II.3: The (max,+) semiring 3 R max is the set R [ f1g, equipped with the operation max, written additively (i.e. a b = max(a; b)) and the usual sum, written multiplicativ... |

298 | Synchronization and Linearity - Baccelli, Cohen, et al. - 1992 |

231 | The Book of Traces. - Diekert - 1995 |

219 | Automata-Theoretic Aspects of Formal Power Series. Texts and Monographs in Computer Science, - Salomaa, Soittola - 1978 |

201 |
Rational series and their languages
- Berstel, Reutenauer
- 1988
(Show Context)
Citation Context ...ated general references. The reader is referred to [2], [15], [42], [30], [25], [23], for an account of the theory of the (max,+) semiring. The theory of automata with multiplicities is dealt with in =-=[4]-=-, [20], [37]. The (max,+) automata used in this paper are generalizations of \cost automata", or automata with multiplicities over the tropical semiring (N [ f+1g;min;+) . They have been widely studie... |

159 | Analysis of Asynchronous Concurrent Systems by Timed Petri Nets. - Ramchandani - 1974 |

154 | Trace theory. - Mazurkiewicz - 1987 |

149 |
A linear-system-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing
- Cohen, Dubois, et al.
- 1985
(Show Context)
Citation Context ... in the system. The most satisfactory results are relative to the subclass of timed Event Graphs, which can be modeled bysnite dimensional recurrent linear systems over the (max,+) semiring, see [2], =-=[12]-=-. There exists a striking connection between the two cases: both (max,+) linear systems and conventional automata are specializations of (max,+) automata, i.e. automata with multiplicities [20] over t... |

148 |
Minmax Algebra
- Cuninghame-Green
- 1979
(Show Context)
Citation Context ...ation algorithm. In x VI, we discuss at a more algebraic level the models used in the paper and their interplay. To conclude, let us mention related general references. The reader is referred to [2], =-=[15]-=-, [42], [30], [25], [23], for an account of the theory of the (max,+) semiring. The theory of automata with multiplicities is dealt with in [4], [20], [37]. The (max,+) automata used in this paper are... |

146 | Concurrent program schemes and their interpretations - Mazurkiewicz - 1977 |

125 | Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. - Desel, Esparza - 1995 |

102 | Automata, Languages, and Machines: Volume A. - Eilenberg - 1974 |

85 |
The Effect of Execution Policies on the Semantics and Analysis of Stochastic Petri Nets.
- Ajmone-Marsan, Balbo, et al.
- 1989
(Show Context)
Citation Context ...sed on time considerations. All logically feasible choices can be considered. This contrasts with several models studied in the literature. For example, in the so-called race policy, see for instance =-=[1]-=-, a place with several output transitions allocates its token to the transition which is able to complete itssringsrst. We denote by (G;M; ) a timed Petri net, where is a map T [P ! R + , providing... |

79 | Graphes et algorithmes. Eyrolles - Gondran, Minoux - 1979 |

49 | Analyse du comportement périodique des systèmes de production par la théorie des dioïdes. Rapport de recherche 191 - Cohen, Dubois, et al. - 1983 |

47 | Performance evaluation of jobshop systems using timed event graphs. - Hillion, Proth - 1989 |

40 | Performance Evaluation of (max,+) Automata. - Gaubert - 1995 |

32 | of pieces. I. Basic definitions and combinatorial lemmas. In Combinatoire énumérative - Heaps - 1985 |

24 | Algebraic system analysis of timed Petri nets.
- Cohen, Gaubert, et al.
- 1995
(Show Context)
Citation Context ...and dynamical equations similar to the ones used here, see the discussion in Remark IV.8 below. A very dierent algebraic approach is that of Baccelli, Foss and Gaujal [3]; Cohen, Gaubert and Quadrat =-=[13]-=-, [14]; and Libeaut and Loiseau, see [29, Chap. 2]. Essentially, the counter function (vector of numbers ofsrings, as a function of time) of general (non-necessarily safe) Free Choice or Fluid Petri n... |

19 | Timed Petri net schedules - Carlier, Chretienne |

18 | Asymptotic throughput of continuous timed petri nets
- Cohen, Gaubert, et al.
- 1995
(Show Context)
Citation Context ...namical equations similar to the ones used here, see the discussion in Remark IV.8 below. A very dierent algebraic approach is that of Baccelli, Foss and Gaujal [3]; Cohen, Gaubert and Quadrat [13], =-=[14]-=-; and Libeaut and Loiseau, see [29, Chap. 2]. Essentially, the counter function (vector of numbers ofsrings, as a function of time) of general (non-necessarily safe) Free Choice or Fluid Petri nets sa... |

13 |
Dynamics of synchronized parallel systems
- Brilman, Vincent
- 1997
(Show Context)
Citation Context ...aton, a special type of (max,+) automaton, the result holding for general, polyomino-shaped, pieces. This was proved in Gaubert and Mairesse [22], and in a dierent form, by Brilman and Vincent [41], =-=[7]-=-. The heap representation theorem for safe timed Petri nets that we give can be seen as a synthesis of these three results. The essential idea is that considering general pieces in heap automata enabl... |

12 | Free Choice Petri Nets: an Algebraic Approach - Baccelli, Foss, et al. - 1996 |

10 |
Speedup of recognizable trace languages
- Cerin, Petit
- 1993
(Show Context)
Citation Context ...al growth rate of the makespan for long schedules) min = lim inf n min w2A n \L y H (w) n ; (20) can (in certain cases) be attacked with automata techniques, either along the lines of Cerin and Petit =-=[11]-=-, or using the determinization techniques of [21]. But the di- culty of the computation of the optimal Lyapunov exponent min if one order of magnitude above that ofsmax . In Eqn (19) and (20), we can... |

8 | Structural, temporal and stochastic properties of unbounded free-choice Petri nets - Baccelli, Foss, et al. - 1994 |

8 | Synchronisation by resources sharing : a performance analysis - Brilman, Vincent - 1995 |

7 |
Reseaux de Petri, Theorie et pratique, Tome 1
- Brams
- 1983
(Show Context)
Citation Context ...ity problems in language theory (see [35], [38], and the references therein). A Discrete Event Systems oriented presentation can be found in [21]. General accounts of Petri net theory can be found in =-=[5]-=-, [33], [16] or in the proceedings [6]. II. Heap Models and (max,+) Automata The following heap model generalizes the heaps of pieces of Viennot [40]. Imagine an horizontal axis with asnite number of ... |

4 | Some ergodic results on stochastic iterative DEDS - Vincent |

1 | Task resourcemodels and(max,+) automata - Mairesse - 1997 |

1 | Timing Analysis andVerification of Timed AsynchronousCircuits - Hulgaard - 1995 |