Bull. Korean Math. Soc. 2010; 47(6): 1251-1258
Printed November 1, 2010
https://doi.org/10.4134/BKMS.2010.47.6.1251
Copyright © The Korean Mathematical Society.
Jeongsim Kim
Chungbuk National University
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.
Keywords: processor-sharing queue, batch arrivals, sojourn time, concavity
MSC numbers: 60K25
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