Modeling and energy consumption evaluation of a stochastic wireless sensor network

In this article, we consider a stochastic model of wireless sensor networks (WSNs) in which each sensor node randomly and alternatively stays in an active mode or a sleep mode. The active mode consists of two phases, called the full-active phase and the semi-active phase. When a referenced sensor node is in the full-active phase of the active mode, it may sense data packets, transmit the sensed packets, receive packets, and relay the received packets. However, when the phase of the sensor node switches from the full active phase to the semi-active phase, it is only able to transmit/relay data. When the referenced sensor node is in a sleep mode, it does not interact with the external world. In this article, first, we develop a stochastic model for the sensor node of a WSN, and then we derive an explicit expression of the stationary distribution of the number of data packets in the sensor node. Furthermore, we figure out some important performance measures, including the sensor node’s energy consumption for transmission, the energy consumption of the sensor operations, and the average energy consumption of the sensor node in a cycle of active and sleep modes. Also, a numerical analysis is provided to validate the proposed model and the results obtained. The novel aspects of our research are the development of a stochastic model for WSN with active and sleep features and the development of important analytical formulae for evaluating the energy consumption of a WSN. These results are expected to be useful as significant contributions to the fundamental theory of the design of various WSNs with active and sleep mode considerations.