The problem of environmental monitoring using a wireless network of chemical sensors with a limited energy supply is considered. Since the conventional chemical sensors in active mode consume vast amounts of energy, an optimisation problem arises in the context of a balance between the energy consumption and the detection capabilities of such a network. A protocol based on dynamic sensor collaboration is employed: in the absence of any pollutant, the majority of sensors are in the sleep (passive) mode; a sensor is invoked (activated) by wake-up messages from its neighbors only when more information is required. The paper proposes a mathematical model of a network of chemical sensors using this protocol. The model provides valuable insights into the network behavior and near optimal capacity design (energy consumption against detection). An analytical model of the environment, using turbulent mixing to capture chaotic fluctuations, intermittency, and nonhomogeneity of the pollutant distribution, is employed in the study. A binary model of a chemical sensor is assumed (a device with threshold detection). The outcome of the study is a set of simple analytical tools for sensor network design, optimisation, and performance analysis.
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