The Effective Coverage of Homogeneous Teams with Radial Attenuation Models

For the area coverage (e.g., using a WSN), despite the comprehensive research works on full-plane coverage using a multi-node team equipped with the ideal constant model, only very few works have discussed the coverage of practical models with varying intensity. This paper analyzes the properties of the effective coverage of multi-node teams consisting of a given numbers of nodes. Each node is equipped with a radial attenuation disk model as its individual model of coverage, which conforms to the natural characteristics of devices in the real world. Based on our previous analysis of 2-node teams, the properties of the effective coverage of 3-node and n-node ((Formula presented.)) teams in regular geometric formations are analyzed as generalized cases. Numerical analysis and simulations for 3-node and n-node teams ((Formula presented.)) are conducted separately. For the 3-node cases, the relations between the side lengths of equilateral triangle formation and the effective coverage of the team equipped with two different types of models are respectively inspected. For the n-node cases ((Formula presented.)), the effective coverage of a team in three formations, namely regular polygon, regular star, and equilateral triangular tessellation (for (Formula presented.)), are investigated. The results can be applied to many scenarios, either dynamic (e.g., robots with sensors) or static, where a team of multiple nodes cooperate to produce a larger effective coverage.