A petri net model with time window constraints

Time window has been a common form of time constraint considered in real world systems. Viewing this requirement, some previous researches on Petri nets included time window constraint into their models by attaching a single time interval to a transition, denoting the time period when the transition may fire after it is enabled. This paper further extends the traditional time-window Petri net model in two respects. First, we extend the time window from a single interval to multiple intervals, that is, a sequence of non-overlapped time intervals is used to denote the periods when the task can be executed. Second, we add the time window constraints into both transitions and places. Specifically, we define a new kind of places, called resource places, and the time window associated with a resource place denotes the time periods when the resource can support task execution. Accordingly, we develop a formal model, named as TWPN (Time Window Petri Net), through which we can model the scenario that multiple cases which share common resources are performed concurrently subject to time windows constraints. Finally, we also show that the model can correctly compute the execution time of each case.