formula /log
, i.e. 2.25/2.3219 = 0.969.
This result can be loosely interpreted as the fact that
uncertainty of sample Petri net reaches 96.9%,
which can be classified as a high degree of
uncertainty. And with that pose problems, such as
low readability, interpretability, predictability, and
other indicators.
6 DISCUSSION
Measurement of uncertainty in process models can
be an indicator for reasoning about the explanatory
power of these models. Mainly the ability to support
different managerial decisions associated with the
prediction of the system behaviour under defined
probabilities (transition matrix). Degree of
uncertainty is usually influenced by a number of
elements that contains a process model. These
elements include OR, XOR, AND, LOOP. Their
arrangement in the process model then implies its
uncertainty. Finally, the main influences for the
amount of uncertainty in the process model are the
probabilities associated witch each branching path
(e.g. OR-split). Another approach of uncertainty
measurement, which uses quantification of
individual substructures in model at different levels
of abstraction, is defined in (Jung et al., 2011). That
approach measures the structural uncertainty of
process models, depending on the location of the
above-mentioned components (OR, AND, etc.).
Approach defined in this work quantifies uncertainty
using concepts of Petri nets with relation to Markov
chains. This approach also allows the measurement
uncertainty in any model that can be modelled as a
Petri net. Thereby is for instance possible to use
multiple tokens in the model or implicitly defined
multiplicity of edges (arcs).
Advantages of this Approach
Universal metric for measuring the uncertainty of
process models that can be modelled using Petri
nets.
The possibility of using the verification features
of Petri nets.
Clearly defined boundaries of uncertainty
(interval0,1.
Possibility to set specific probabilities for
branching in the model.
Disadvantages of this Approach
Fundamental deficiencies of Petri nets in general,
i.e. state explosion, restrictions based on
definitions, etc.
7 CONCLUSIONS AND FUTURE
WORK
In this paper was defined method for calculating the
uncertainty of any process model, which can be
modelled by Petri net. The actual uncertainty
quantification is based on the measurement of
entropy on the set of all reachable marking of Petri
net and its steady-state probabilities. On the prime
example is presented the calculation of the
uncertainty.
One of the relative weaknesses of this approach
is non-implicit definition of branching probabilities,
i.e. the need to explicitly define these probabilities in
the transition matrix (or not consider probabilities at
all). Therefore, the future research will be focused
on defining this method using stochastic Petri nets,
which implicitly define probability rates of
transitions in its definition.
ACKNOWLEDGEMENTS
This work was supported by the project
No. CZ.1.07/2.2.00/28.032 Innovation and support
of doctoral study program (INDOP), financed from
EU and Czech Republic funds.
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