Battery lifetimes in wireless sensor networks are dictated by usage patterns and the elected transmission power. As batteries fail there is an inevitable devolution of the network characterized by the growth of sensory lacunae or dead spots in the sensor field and eventually a breakdown in connectivity between the surviving nodes of the network. Sharp limit theorems characterizing the time at which these phenomena make their appearance are derived. These results provide explicit fundamental tradeoffs between transmission power, node density, and battery design and suggest how efficient choices may be made.
Date of this Version
Date Posted: 04 August 2005