Firing and enabling sequences estimation for timed Petri nets

Petri nets (PNs) are useful tools for the modeling and analysis of discrete event systems, This work deals with the estimation of firing and enabling sequences for timed transition PNs with unknown time delays. The marking and the reserved marking of the places are measured on line. The estimation problem has exact and approximated solutions that are described, Sufficient conditions are given on the measurement accuracy of the marking and reserved marking vectors, so that the estimation of firing and enabling sequences is an exact one. If the estimation provides several solutions, the PN is extended in order to give a unique solution, Numerical aspects of the estimation are also investigated. As a consequence of this, the proposed method provides interesting tools for the modeling, the performance analysis, and above all the monitoring of manufacturing systems and roadway traffic networks.