Non-stationary behavior of departure process in a finite-buffer MX/G/1/K-type queueing model with batch arrivals, in which a threshold-type waking up N-policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the Nth message occurrence, where the threshold value N is fixed. Using the analytical approach based on the idea of an embedded Markov chain, integral equations, continuous total probability law, renewal theory and linear algebra, a compact-form representation for the mixed double transform (probability generating function of the Laplace transform) of the probability distribution of the number of messages completely served up to fixed time t is obtained. The considered queueing system has potential applications in modeling nodes of wireless sensor networks (WSNs) with battery saving mechanism based on threshold-type waking up of the radio. An illustrating simulational and numerical study is attached.