Concavity of the conditional mean sojourn time in the processor-sharing queue with batch arrivals

Jeongsim Kim

doi:10.4134/BKMS.2010.47.6.1251

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Bull. Korean Math. Soc. 2010; 47(6): 1251-1258

Printed November 1, 2010

https://doi.org/10.4134/BKMS.2010.47.6.1251

Concavity of the conditional mean sojourn time in the processor-sharing queue with batch arrivals

Jeongsim Kim

Chungbuk National University

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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.

Keywords: processor-sharing queue, batch arrivals, sojourn time, concavity

MSC numbers: 60K25