An Alternative View of Fairness in Petri Nets

Ibl, Martin

doi:10.1145/2641483.2641515

Cited by 2 publications

(3 citation statements)

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“…Over the past ten years, the research area that addresses the measurement of the process of non-functional characteristics has expanded. These non-functional characteristics are, for example, the complexity [12,13], uncertainty [14,15], cohesion [16], and fairness [17]. These characteristics are used for the quantification of the system properties, such as user-friendliness, usability, comprehensibility, and predictability [18].…”

Section: Complexity Measuresmentioning

confidence: 99%

“…For the basic Place/Transition, timed and stochastic Petri nets exist an analytical approach for the calculation of stationary probabilities, and for the higher classes (e.g., generalized stochastic Petri nets), simulation must be used to approximate the stationary probabilities. In the following, we present the abbreviated procedure for the quantification of stationary probabilities for Place/Transition Petri net models, which can be found in full in [17]. The procedure for the quantification of the stationary probabilities for stochastic Petri nets can be found in [15].…”

Section: The Quantification Of Stationary Probabilitiesmentioning

confidence: 99%

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A Behavioural Analysis of Complexity in Socio-Technical Systems under Tension Modelled by Petri Nets

Ibl

Čapek

2017

Entropy

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Complexity analysis of dynamic systems provides a better understanding of the internal behaviours that are associated with tension and efficiency, which in the socio-technical systems may lead to innovation. One of the popular approaches for the assessment of complexity is associated with self-similarity. The dynamic component of dynamic systems represents the relationships and interactions among the inner elements (and its surroundings) and fully describes its behaviour. The approach used in this work addresses complexity analysis in terms of system behaviour, i.e., the so-called behavioural analysis of complexity. The self-similarity of a system (structural or behavioural) can be determined, for example, using fractal geometry, whose toolbox provides a number of methods for the measurement of the so-called fractal dimension. Other instruments for measuring the self-similarity in a system, include the Hurst exponent and the framework of complex system theory in general. The approach introduced in this work defines the complexity analysis in a social-technical system under tension. The proposed procedure consists of modelling the key dynamic components of a discrete event dynamic system by any definition of Petri nets. From the stationary probabilities, one can then decide whether the system is self-similar using the abovementioned tools. In addition, the proposed approach allows for finding the critical values (phase transitions) of the analysed systems.

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Section: Complexity Measuresmentioning

confidence: 99%

Section: The Quantification Of Stationary Probabilitiesmentioning

confidence: 99%

A Behavioural Analysis of Complexity in Socio-Technical Systems under Tension Modelled by Petri Nets

Ibl

Čapek

2017

Entropy

Self Cite

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“…These characteristics include, for instance, complexity [1,2], uncertainty [3], cohesion [4] or fairness [5]. These metrics are then used to analyse user-friendliness, usability, comprehensibility, predictability and other indicators [6].…”

Section: Introductionmentioning

confidence: 99%

Measure of Uncertainty in Process Models Using Stochastic Petri Nets and Shannon Entropy

Ibl

Čapek

2016

Entropy

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When modelling and analysing business processes, the main emphasis is usually put on model validity and accuracy, i.e., the model meets the formal specification and also models the relevant system. In recent years, a series of metrics has begun to develop, which allows the quantification of the specific properties of process models. These characteristics are, for instance, complexity, comprehensibility, cohesion, and uncertainty. This work is focused on defining a method that allows us to measure the uncertainty of a process model, which was modelled by using stochastic Petri nets (SPN). The principle of this method consists of mapping of all reachable marking of SPN into the continuous-time Markov chain and then calculating its stationary probabilities. The uncertainty is then measured as the entropy of the Markov chain (it is possible to calculate the uncertainty of the specific subset of places as well as of whole net). Alternatively, the uncertainty index is quantified as a percentage of the calculated entropy against maximum entropy (the resulting value is normalized to the interval <0,1>). The calculated entropy can also be used as a measure of the model complexity.

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An Alternative View of Fairness in Petri Nets

Cited by 2 publications

References 10 publications

A Behavioural Analysis of Complexity in Socio-Technical Systems under Tension Modelled by Petri Nets

A Behavioural Analysis of Complexity in Socio-Technical Systems under Tension Modelled by Petri Nets

Measure of Uncertainty in Process Models Using Stochastic Petri Nets and Shannon Entropy

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