Kybernetika 58 no. 1, 82-100, 2022

Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism

Wojciech M. Kempa and Dariusz KurzykDOI: 10.14736/kyb-2022-1-0082


Non-stationary behavior of departure process in a finite-buffer $M^{X}/G/1/K$-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 $N$th 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.


transient state, departure process, finite-buffer queue, $N$-policy, power saving, wireless sensor network (WSN)


60K25, 90B22


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