Accuracy Measures for Timed Petri Nets

The paper is in the scope of quality assessment of discrete-event process models; accuracy measures of timed Petri nets (TPN) are proposed. A TPN <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{N}$</tex> is assessed concerning a set of dated event sequences <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda_{\tau}$</tex>, where the occurrence instant of every event is recorded. The class of TPN addressed assigns real-valued time parameters to transitions as a single value <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\delta}(\mathbf{t}_{\mathbf{j}})$</tex> or an interval of values <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\imath(\mathbf{t}_{\mathbf{j}})$</tex>; a metric is developed for each kind of timing. The accuracy of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{N}$</tex> is evaluated on [0, 1] by measuring the deviations between the actual event occurrences in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\lambda}_{\boldsymbol{\tau}}$</tex> and the expected firing instant of transitions in the TPN.