Abstract
We study a multiclass single-server retrial system with independent Poisson inputs and the state-dependent retrial rates. Meeting busy server, a new class-i customer joins orbit i. Orbit i is working as a FIFO-type queueing system, in which the top customer retries to occupy server. The retrial times are exponentially distributed with a rate depending on the current configuration of the binary states of all orbits, idle or non-idle. We present a new coupling-based proof of the necessary stability conditions of this retrial system, found earlier in the paper [17]. The key ingredient of the proof is a coupling of the processes of retrials with the corresponding independent Poisson processes. This result allows to apply classic property PASTA in the following performance analysis. A few numerical results verifying stability conditions of a 3-class system are included as well.
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Acknowledgements
The study was carried out under state order to the Karelian Research Centre of the Russian Academy of Sciences (Institute of Applied Mathematical Research KRC RAS). The research of is partly supported by Russian Foundation for Basic Research, projects 18-07-00147, 18-07-00156, 19-07-00303.
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Morozov, E., Morozova, T. (2019). A Coupling-Based Analysis of a Multiclass Retrial System with State-Dependent Retrial Rates. In: Phung-Duc, T., Kasahara, S., Wittevrongel, S. (eds) Queueing Theory and Network Applications. QTNA 2019. Lecture Notes in Computer Science(), vol 11688. Springer, Cham. https://doi.org/10.1007/978-3-030-27181-7_3
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