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Concavity of the conditional mean sojourn time in the M/G/1 processor-sharing queue with batch arrivals

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Abstract

Avrachenkov et al. (Queueing Syst. 50:459–480, [2005]) conjectured that in an M/G/1 processor-sharing queue with batch arrivals, the conditional mean sojourn time is concave. In this paper, we show that this conjecture is generally not true.

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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 work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-312-C00470).

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Kim, J., Kim, B. Concavity of the conditional mean sojourn time in the M/G/1 processor-sharing queue with batch arrivals. Queueing Syst 58, 57–64 (2008). https://doi.org/10.1007/s11134-007-9058-1

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  • DOI: https://doi.org/10.1007/s11134-007-9058-1

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