Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CONCAVITY OF THE CONDITIONAL MEAN SOJOURN TIME IN THE PROCESSOR-SHARING QUEUE WITH BATCH ARRIVALS

  • Kim, Jeong-Sim (DEPARTMENT OF MATHEMATICS EDUCATION CHUNGBUK NATIONAL UNIVERSITY)
  • Received : 2009.04.19
  • Published : 2010.11.30
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Abstract

For an M/G/1 processor-sharing queue with batch arrivals, Avrachenkov et al. [1] conjectured that the conditional mean sojourn time is concave. However, Kim and Kim [5] showed that this conjecture is not true in general. In this paper, we show that this conjecture is true if the service times have a hyperexponential distribution.

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References

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