On buffer overflow duration in WSN with a vacation-type power saving mechanism

A queue-based model of WSN's node with power saving mechanism described by the single vacation policy is considered. Whenever the queue of packets directed to the node becomes empty, the radio transmitter/receiver is being switched off for a random and generally distributed time period. During the vacation the processing is blocked and the incoming packets are buffered. Modelling the transient behavior of the node by an M/G/1/N-type system with single server vacations, the CDF (cumulative distribution function) of buffer overflow duration, conditioned by the initial buffer state, is investigated. Applying analytical approach based on the idea of embedded Markov chain, integral equations and linear algebra, the compact-form representation for the first buffer overflow duration CDF is found. Hence, the formula for the CDF of next such periods is derived. Moreover, probability distributions of the number of packet losses in successive buffer overflow periods are found. Numerical example is attached as well.