Metric for Calculation of System Complexity based on its Connections

Abstract

This paper proposes a methodology based on system connections to calculate its complexity. Two study cases are proposed: the dining Chinese philosophers’ problem and the distribution center. Both studies are modeled using the theory of Discrete Event Systems and simulations in different contexts were performed in order to measure their complexities. The obtained results present i) the static complexity as a limiting factor for the dynamic complexity, ii) the lowest cost in terms of complexity for each unit of measure of the system performance and iii) the output sensitivity to the input parameters. The associated complexity and performance measures aggregate knowledge about the system.

Complexity measure based on sensitivity analysis applied to an intensive care unit system

“…Considering the system under study, Lloyd 35 lists forty system complexity metrics in three groups: (i) description difficulty, (ii) creation difficulty, and (iii) degree of organization. Complexity metrics can be based on entropy 36 , degree of hierarchy 10 , algorithmic information content 37 , 38 , computational capacity 39 , thermodynamic depth 40 , statistics 41 , fractal dimension 42 , logical depth 43 , dynamic depth 5 , amount of information 31 , size 8 , and connections 44 .…”

Complexity Measure based on Sensitivity Analysis Applied to an Intensive Care Unit system

“…Considering the system under study, Lloyd 38 lists forty system complexity metrics in three groups: (i) description difficulty, (ii) creation difficulty, and (iii) degree of organization. Complexity metrics can be based on entropy 39 , degree of hierarchy 10 , algorithmic information content 40,41 , computational capacity 42 , thermodynamic depth 43 , statistics 44 , fractal dimension 45 , logical depth 46 , dynamic depth 5 , amount of information 34 , size 8 , and connections 47 .…”

Mechanism for Measuring System Complexity Applying Sensitivity Analysis

“…The complexity measures are used to compare systems or different configurations of the same system [13,32]. In some cases, these measures are dimensionless, allowing to compare one value to another one measured in the same system or in different systems, as long as the nature of them allows comparison [32,33].…”

“…Some complexity metrics are proposed based on the information entropy [32,[34][35][36][37]. Considering the system connections, Paiva [33] presents the modeling of Shannon [38] adapted by Lemes [35] to measure the system complexity using…”

“…Based on the Paiva's [33] modeling, the proposed method measures the complexity of real systems using expression (2). This metric considers the connections regardless of information exchange, observing their probabilities according to expression (3).…”