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Stability of a multi-class multi-server retrial queueing system with service times depending on classes and servers

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Abstract

We consider a multi-class multi-server retrial queueing system. Customers of each class arrive from outside the system according to a Poisson process. The service times for each class of customers are assumed to be exponentially distributed with service rates depending on both the customers’ class and the servers. We define the offered load and provide stability and instability conditions for this retrial queueing system. The stability result can be obtained by introducing artificial primitive processes and using the fluid limit approach.

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Acknowledgements

We are grateful to the reviewer for valuable comments and suggestions. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1A2B4012676). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03029542).

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Authors and Affiliations

  1. Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, Korea

    Bara Kim

  2. Department of Mathematics Education, Chungbuk National University, 1 Chungdae-ro, Seowon-gu, Cheongju, Chungbuk, 28644, Korea

    Jeongsim Kim

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  1. Bara Kim
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  2. Jeongsim Kim
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Correspondence to Jeongsim Kim.

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Kim, B., Kim, J. Stability of a multi-class multi-server retrial queueing system with service times depending on classes and servers. Queueing Syst 94, 129–146 (2020). https://doi.org/10.1007/s11134-019-09634-x

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  • DOI: https://doi.org/10.1007/s11134-019-09634-x

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