The various approaches in time modelling in Petri nets are successively presented. Then an example is proposed to illustrate the modelling constructs. Qualitative and quantitative. In linear time you only describe chaining of actions along the time axial while in branching time several different futures can occur and you described how and when the branching is made among the set of possible futures. The state of the system is given by the marking of the net, which is a distribution of tokens in the net's places.
State changes result from the firing of transitions, yielding a new distribution of tokens.
A transition is enabled to fire when all of its input places contain tokens. Those approaches allow to state temporal relationships between actions, such as before , after and meanwhile . Figure 1 describes a total ordering between actions A and B, stating that actions B may start only after A has completed, thus showing how After and Before constructs are modelled using Petri nets. Hierarchical refinement allows constructing such complex structures out of basic constructs as illustrated in Figure 3. Modelling Qualitative time modelling is concerned about precedence, sequences and interleaving between actions.