Firing sequences and firing frequencies estimation for timed Petri nets

Petri nets are useful tools for the modelling and analysis of manufacturing systems. This work deals with the firing sequences estimation for transiti ons-timed Petri nets by measurement of the places marking. Firing durations are unknown, but not supposed to be null. In fact, the Petri net marking i s measured, on-line, with a sampling period Delta t small enough such that each transition is fired, at the most, one time during Delta t. The estimat ion problem has exact and approximated solutions that are described. Suffic ient conditions are given on the accuracy of the marking measurement, such that the estimation of the firing sequences is an exact one. If the estimat ion provides several solutions, the Petri net is completed in order to give one unique solution. Lastly, the firing sequences estimation is used to ev aluate the transition firing occurrences and the firing frequencies. As a c onsequence of this, the proposed method provides the machine's occupation r ate for manufacturing and assembly workshops modelled by timed Petri nets. Thus, systems performances are evaluated and can be improved with the help of these results. The firing sequences estimation is also interesting for f ault diagnosis and timed Petri nets identification.