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

Abstract

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.

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

“…Other instruments for measuring the self-similarity in a system include the Hurst exponent. The other methods for complexity analysis and its comparison are introduced in detail, for example, in our previous work [15].…”

“…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].…”

“…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].…”

Using Entropy in Web Usage Data Preprocessing

“…The proposed minimax entropy model is used to estimate the parameters with the preference learning. Ibl and Capek [ 19 , 20 ] used level of uncertainty (entropy) as an indicator for determining the degree of predictability of modelled systems. The authors focused on measuring the uncertainty of a process model that was modelled using stochastic Petri nets.…”

Measurement of the uncertainty

“…Alternatively, the uncertainty index is quantified as a percentage of the calculated entropy versus the maximum entropy (the resulting value is normalized to the interval <0.1>). Calculated entropy can also be used as a measure of model complexity [7].…”