D–timed Petri Nets and Modelling of Timeouts and Protocols

D–timed Petri nets are Petri nets with deterministic firing times assigned to transitions of a net. Several classes of D–timed are discussed in this paper to show a hierarchy of models with increasing “modelling power”. Conflict–free inhibitor nets are sufficient to model communication protocols with timeouts used to recover from lost and/or distorted messages but they introduce intermediate states which can be removed without any significant effect on the model’s behaviour. Extended nets with interrupt arcs (or generalized inhibitor arcs) eliminate all such states. Finally, enhanced nets with two classes of transitions, immediate and timed transitions, are introduced to further reduce the state space. For each class a discrete–time description is provided which represents the behaviour of a net by a homogeneous semi–Markov discrete process. Many performance characteristics can thus be obtained using an approach similar to operational analysis.