Several Characteristics of Active/Sleep Model in Wireless Sensor Networks

We investigate several characteristics of active/sleep model in wireless sensor networks (WSNs). Here, each node of the investigated WSN may be randomly and alternatively in an ACTIVE status or a SLEEP status. When a referenced sensor node is in an ACTIVE status, it may generate data packets with a given stochastic process and may transmit/receive a data packet with a random period of time. However, when the referenced sensor node is in a SLEEP status, it may only be able to stochastically generate date packets but not transmit/receive. If all possible next-hop nodes of the referenced node are in SLEEP statuses, we will say the environment of the referenced node to be in an OFF period. If there exists at least one next-hop node of the referenced node to be in ACTIVE status, we will say that its environment is in an ON period. In this shorter paper, we first derive the steady-state probability distribution of number of data packets in the referenced node and then obtain the distribution function for a node to be in an ON period and in an OFF period, respectively. The novelty of this note is in its development of a stochastic model in WSN with active/sleep feature and the explicit results obtained for above two performance characteristics. These results are expected to be useful as the fundamental results in the theoretic analysis and design of various WSNs with active and sleep status consideration.