Timestamp nets in technical applications

Timestamp Petri nets, introduced in this paper, offer a new method to deal with time critical problems in the field of automation of manufacturing systems. To each token in a timestamp net a timestamp is assigned, which denotes the time when the token was put on its place. In those nets intervals are assigned to the incoming edges of transitions, which describe the permeability of the edge relative to the token on the adjacent place. In timestamp nets it is possible that synchronizing transitions are not able to fire although they are supplied with tokens sufficiently, because their incoming edges are not permeable simultaneously. In this case we say the transition got timewise stuck. In this paper it is examined how transitions of a timestamp net are getting timewise stuck. Based on a symbolic analysis, these investigations can be reduced to solving systems of linear inequalities. The method can also be used to determine parameters for a timestamp net in order to prevent transitions from getting timewise stuck. We show the method´s applicability by the dynamic model of a small technical plant as an example. Forbidden states of the uncontrolled system are described by transitions which can get timewise stuck. We use the method to determine time parameters of a controller, which ensures that forbidden states in the controlled system are unreachable.