![](bg6.png)
The need to specify amongst which places the
fairness will be measured and what the
resulting value of fairness represents.
7 CONCLUSION AND FUTURE
WORK
Measuring of fairness in the process model can be a
good indicator for overload detection of different
nodes in the model (bottleneck, overwork, etc.)
In this paper has been defined method for
calculating the fairness of any process model, which
can be modelled by stochastic Petri net. Defined
method can be applied to a specific sublet of places,
as well as the whole Petri net.
The actual fairness quantification is based on the
measurement of entropy from steady-state
probabilities of all places (or a specific subset of
places). On the prime example is presented the
calculation of the fairness.
The future research will be focused on defining
this method using coloured Petri nets, which allow
diversification of tokens. This allows measurement
of fairness for entities that provide process (states)
as well as entities that are subjects in the process
(tokens).
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.
REFERENCES
"Fairness", 2011. Oxford Advanced American Dictionary
for learners of English
Alpern, B., Schneider, F. B., 1985. Defining liveness.
Information Processing Letters, 21, 181-185.
Apt, K., Francez, N., Katz, S., 1988. Appraising fairness
in languages for distributed programming. Distributed
Computing, 2, 226-241.
Avi-Itzhak, B., Levy, H., Raz, D., 2008. Quantifying
fairness in queuing systems: Principles, approaches,
and applicability. Probab. Eng. Inf. Sci., 22, 495-517.
Baier, C., Katoen, J.-P., 2008. Principles of model
checking, Cambridge, Mass., The MIT Press.
González, L. S., Rubio, F. G., González, F. R., Velthuis,
M. P., 2010. Measurement in business processes: a
systematic review. Business Process Management
Journal, 16, 114 - 134.
Ibl, M., 2013. Uncertainty Measure of Process Models
using Entropy and Petri Nets. ICSOFT 2013 -
Proceedings of the 8th International Joint Conference
on Software Technologies, 2013. Setubal: Institute for
Systems and Technologies of Information, Control and
Communication (INSTICC), 542-547.
Jaffe, J., 1981. Bottleneck Flow Control. Communications,
IEEE Transactions on, 29, 954-962.
Jung, J.-Y., Chin, C.-H., Cardoso, J., 2011. An entropy-
based uncertainty measure of process models.
Information Processing Letters, 111, 135-141.
Kelly, F., 1997. Charging and rate control for elastic
traffic. European Transactions on
Telecommunications, 8, 33-37.
Larson, R. C., 1987. PERSPECTIVES ON QUEUES -
SOCIAL-JUSTICE AND THE PSYCHOLOGY OF
QUEUING. Operations Research, 35, 895-905.
Lassen, K. B., Van Der Aalst, W. M. P., 2009. Complexity
metrics for Workflow nets. Information and Software
Technology, 51, 610-626.
Marsan, M. A., 1990. Stochastic Petri nets: an elementary
introduction. In: GRZEGORZ, R. (ed.) Advances in
Petri nets 1989. Springer-Verlag New York, Inc.
Molloy, M. K., 1982. Performance Analysis Using
Stochastic Petri Nets. Computers, IEEE Transactions
on, C-31, 913-917.
Palm, C., 1953. Methods of Judging the Annoyance
Caused By Congestions. TELE (English ed.), 1-20.
Petri, C. A., 1962. Kommunikation mit Automaten.
Bonn:
Institut für Instrumentelle Mathematik, Schriften des
IIM Nr. 2.
Raz, D., Levy, H., Avi-Itzhak, B., 2004. A resource-
allocation queueing fairness measure. SIGMETRICS
Perform. Eval. Rev., 32, 130-141.
Reijers, H. A., Vanderfeesten, I. T. P., 2004. Cohesion and
Coupling Metrics for Workflow Process Design. In:
DESEL, J., PERNICI, B. & WESKE, M. (eds.)
Business Process Management. Springer Berlin
Heidelberg.
Shannon, C. E., 1948. A mathematical theory of
communication. Bell System Technical Journal, 27,
379-423.
Völzer, H., Varacca, D., 2012. Defining Fairness in
Reactive and Concurrent Systems. Journal of the
ACM, 59, 13-13:37.
ICSOFT-PT2014-9thInternationalConferenceonSoftwareParadigmTrends
120