Abstract
We consider an \(\textit{M/G/1}\) retrial queueing system with two classes of customers, in which the service time distributions are different for both classes of customers. When the server is unavailable, an arriving class-1 customer is queued in the queue with infinite capacity, whereas class-2 customer enters the retrial group. In this paper, we are concerned with the analysis of the waiting time distribution. We obtain the joint transform of the waiting time of a class-2 customer and the number of class-2 customers as well as the Laplace–Stieltjes transform of the waiting time of a class-1 customer. We also obtain all the moments of the waiting time distributions of class-1 and class-2 customers.
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Acknowledgments
We are grateful to the reviewers for their valuable comments and suggestions, which improved this paper. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01005831). 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 (2014R1A1A4A01003813).
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Kim, B., Kim, J. Waiting time distributions in an M/G/1 retrial queue with two classes of customers. Ann Oper Res 252, 121–134 (2017). https://doi.org/10.1007/s10479-015-1979-1
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DOI: https://doi.org/10.1007/s10479-015-1979-1