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The matched queueing system GIoPh/Ph/1

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Abstract

We study the matched queueing system GIoPH/PH/1, where the type-I input is a renewal process, the type-II input is a PH renewal process, and the service times are i.i.d. random variables with PH-distributions. First, a condition is given for the stationarity of the system. Then the distributions of the number of type-I customers at the arrival epoches of type-I customers and the number of type-I customers at an arbitrary epoch are derived. We also discuss the occupation time and the waiting time. Their L.S. transforms are derived. Finally, we discuss some problems in numerical computation.

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Authors and Affiliations

  1. Institute of Applied Mathematics, the Chinese Academy of Sciences, 100080, Beijing, China

    Xu Guanghui (Guang-Hui Hsu) & He Qiming

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  1. Xu Guanghui (Guang-Hui Hsu)
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  2. He Qiming
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This research is supported by the National Natural Science Foundation of China and partially by the Institute of Mathematics, the Chinese Academy of Sciences.

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Xu, G.(H.H., He, Q. The matched queueing system GIoPh/Ph/1. Acta Mathematicae Applicatae Sinica 10, 34–47 (1994). https://doi.org/10.1007/BF02006257

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  • DOI: https://doi.org/10.1007/BF02006257

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