New perspectives in time(d) Petri nets and their analysis

Time(d) Petri nets (PNs) modify the basic PN semantics to model temporal relations and constraints of a system. This paper shows how to model these relations without modifying the basic definition of PNs, and is an extension of another paper, where time is represented as a state of a system, to improve its analysis methods. Temporal and logical relations are naturally intertwined, enabling the conventional reachability analysis to be used for answering such questions such as "can the system finish all the jobs within a specified period of time?" The firing of a transition, called clock, models clock ticking. It deposits tokens, i.e. time units, to some places. The output transitions of these places model finishing of the events and their corresponding arc weights model the amount of time needed to finish these events. It is possible to model scheduling of due dates and to calculate tardiness. The reachability analysis is also improved through transforming a PN into conflict-free subnets by duplicating some places and transitions, if the transformation is possible and efficient, to find firing sequences leading to target markings and deadlocks. Another technique for the reachability analysis is also discussed where there is no need for creating conflict-free subnets.