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Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication

  • S.I.: QueueStochMod2019
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Abstract

We consider an M/G/1 retrial queue in which there are two types of calls: ingoing calls made by regular customers and outgoing calls made by the server in idle time. The service times of ingoing calls and outgoing calls have different arbitrary distributions. In this paper, we are interested in the analysis of the waiting time distribution. We obtain an equation for the joint transform of the number of ingoing calls in the orbit and the waiting time of an arbitrary ingoing call. Using this result, we can obtain the moments of the waiting time distribution of an arbitrary ingoing call.

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Acknowledgements

We are grateful to the reviewers for valuable comments and suggestions. S.W. Lee’s research was supported by the Pukyong National University Research Fund in 2019 (C-D-2019-1249). B. Kim’s research was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government(MSIT) (No. 2020R1A2B5B01001864). J. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568).

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Authors and Affiliations

  1. Division of Business Administration, Pukyong National University, 45 Yongso-ro, Nam-gu, Busan, 48513, Korea

    Se Won Lee

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

    Bara Kim

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

    Jeongsim Kim

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  1. Se Won Lee
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Correspondence to Jeongsim Kim.

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Lee, S.W., Kim, B. & Kim, J. Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication. Ann Oper Res 310, 505–518 (2022). https://doi.org/10.1007/s10479-020-03717-2

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  • DOI: https://doi.org/10.1007/s10479-020-03717-2

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