Occurrence Graphs for Interval Timed Coloured Nets

We present an approach to construct the occurrence graph for ITCPN (Interval Timed Coloured Petri Nets). These models, defined by Van Der Aalst in [VAN] can simulate other timed Petri nets and allow to describe large and complex real-time systems. We define classes as sets of states between two occurrences, and we use these classes to define the occurrence graph of an ITCPN. Then an equivalence relation based on time is defined for classes, and we show that occurrence graphs reduced using this equivalence relation are finite if and only if the set of reachable markings is finite. These graphs can be used to verify all the dynamic properties such as reachability, boundedness, home, liveness and fairness properties but also performance properties: minimal and maximal bounds along a occurrence sequence or a cycle. Finally we complete delay based equivalence with a colour based equivalence in order to achieve further reduction.