Analysis of the Battery Level in Complex Wireless Sensor Networks Using a Two Time Scales Second Order Fluid Model

Battery operated Wireless Sensor Networks (WSNs) are currently one of the most important research areas related to applications: the possibility of running complex algorithms and off-load tasks using Fog and Edge computing techniques, as well as the ability of increasing the battery lifetime adopting energy harvesting, together with the communication capabilities offered by infrastructures such as 5G, are just some of the reasons for which this topic continues to be one of the most challenging and interesting. In this paper we focus on the problem of modeling the battery evolution of the devices, focusing on the issues created by the two time scales at which system evolves: tasks execution, sensor readings, and network operations occur at a small time scale, while energy harvesting and battery depletion runs on a much larger time frame. We propose a fluid model for the entire system, and we analyze it in two steps: we first focus on the small time scales to produce a simplified Second Order Fluid Model (SOFM), which later is used to reproduce the evolution at the large time frame. We analyze the considered models using discrete event simulation.