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Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure

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Abstract

This paper discusses the asymptotic behavior of the loss probability for general queues with finite GI/M/1 type structure such as GI/M/c/K, SM/M/1/K and GI/MSP/1/K queues. We find an explicit expression for the asymptotic behavior of the loss probability as K tends to infinity. With the result, it is shown that the loss probability tends to 0 at a geometric rate.

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Authors and Affiliations

  1. Department of Mathematics Education, Chungbuk National University, 12, Gaeshin-dong, Heungduk-ku, Cheongju, Chungbuk, 361-763, Republic of Korea

    Jeongsim Kim

  2. Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Republic of Korea

    Bara Kim

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

Additional information

This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).

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Kim, J., Kim, B. Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure. Queueing Syst 57, 47–55 (2007). https://doi.org/10.1007/s11134-007-9045-6

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  • DOI: https://doi.org/10.1007/s11134-007-9045-6

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