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Tail asymptotics for the queue size distribution in a discrete-time Geo/G/1 retrial queue

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Abstract

We consider a discrete-time Geo/G/1 retrial queue where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically geometric. Remarkably, the result is inconsistent with the corresponding result in the continuous-time counterpart, the M/G/1 retrial queue, where the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function.

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Authors and Affiliations

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

    Bara Kim

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

    Jeongsim Kim

Authors
  1. Bara Kim
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  2. Jeongsim Kim
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Correspondence to Jeongsim 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) and the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2008-314-C00031).

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Kim, B., Kim, J. Tail asymptotics for the queue size distribution in a discrete-time Geo/G/1 retrial queue. Queueing Syst 61, 243–254 (2009). https://doi.org/10.1007/s11134-009-9106-0

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  • DOI: https://doi.org/10.1007/s11134-009-9106-0

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