Abstract
In this research we demonstrate how the regenerative methodology allows to deduce stability conditions in some particular queueing models by a unified way. First we consider the retrial system with classical retrial discipline in which the retrial times becomes exponential when the orbit size exceeds a high threshold. Then we study the buffered system with a state-dependent arrival rate, and finally, a buffered batch-arrival and batch-service system with random serving capacity and batch-size-dependent service. We present short transparent regenerative proofs of the stability conditions of these systems which have been obtained in previous works by various methods. Some numerical examples are given.
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References
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The paper was published with the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement № 075-15-2022-284.
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Rogozin, S., Morozov, E. (2023). A Unified Regenerative Stability Analysis of Some Non-conventional Queueing Models. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks. DCCN 2022. Communications in Computer and Information Science, vol 1748. Springer, Cham. https://doi.org/10.1007/978-3-031-30648-8_24
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