System dynamics baseline model for determining a multivariable objective function optimization in Wireless Sensor Networks

Wireless Sensor Networks (WSN) are dedicated networks used in applications where environmental information must be collected, such as temperature, humidity, level, flow, pressure, rain, radiation, among others. These kinds of networks are constrained regarding power, bandwidth, number of nodes per area unit, etc. It is desirable that they operate without supervision and can work steadily in time, because they are normally located in difficult or far places. Nonetheless, some of these metrics are conflicting with others, so if one improves, some of the others get worse. So, it is mandatory to know what is the best combination of metrics that in conjunction can fit an application the best. Literature reports works where \neg optimization is used as a mathematical scheme to solve this problem, and two scenarios are provided: First, where a single objective function is proposed regarding one metric, and the other metrics are restricted via constraints, and second, where multi-objective optimization (MOOP) approaches are proposed, but without considering the whole set of significant metrics involved in WSN, so there is not a definitive solution that finds a real optimal set of metrics. System Dynamics (SD) is a computer-aided approach to design and analyze (mostly) social, economic and enterprise systems, that allows proposing a mathematical framework to analyze such complex systems, by using relationships of interdependence, mutual interaction, feedback and causality. This work aims to show a first dynamic hypothesis of a model that considers important metrics ofWSN, in order to find a set of equations that serve as objective functions in a MOOP context. By applying this methodology is possible to find some difficult relations between metrics, that are not clearly reported by previous work so far.