Geodesic
Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism
Kybernetika, Tome 58 (2022) no. 1, pp. 82-100.

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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.
DOI : 10.14736/kyb-2022-1-0082
Classification : 60K25, 90B22
Keywords: departure process; finite-buffer queue; $N$-policy; power saving; transient state; wireless sensor network (WSN) 
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     title = {Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism},
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Kempa, Wojciech M.; Kurzyk, Dariusz. Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism. Kybernetika, Tome 58 (2022) no. 1, pp. 82-100. doi : 10.14736/kyb-2022-1-0082. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2022-1-0082/

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