Time-dependent analysis of transmission process in a wireless sensor network with energy saving mechanism based on threshold waking up

Transient departure process of outgoing packets in a node of a wireless sensor network with energy saving mechanism based on threshold activation of the radio transmitter/receiver is investigated. A finite-buffer queueing system of the GI/M/1-type with N-policy, in which the transmission after each idle period is being initialized only after reaching a threshold of N packets waiting in the buffer, is considered as a mathematical model of the node operation. Applying the analytical approach based on the paradigm of embedded Markov chain, total probability law, linear algebra and renewal theory, a compact-form representation for the mixed double transform of probability distribution of the number of packets transmitted down the node till fixed time epoch is derived. A numerical illustrating example is attached as well.