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

  • Authors:

  • Jeongsim Kim;Bara Kim

  • Affiliations:

  • Department of Mathematics Education, Chungbuk National University, Chungbuk, Republic of Korea 361-763;Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, Seoul, Republic of Korea 136-701

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2008

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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.