Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue

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Abstract

This paper studies the M/G/1 processor-sharing (PS) queue and the sojourn time distribution conditioned on the initial job size. Although several expressions for the Laplace-Stieltjes transform (LST) are known, these expressions are not applicable for computational purposes. This paper derives readily applicable expressions for insensitive bounds of \textit{all} moments of the conditional sojourn time distribution. The \textit{instantaneous} sojourn time, the sojourn time of a very small job, leads to insensitive upper bounds with special structure requiring only knowledge of the traffic load and the initial job size. Interestingly, the special form of the upper bounds involves polynomials with so-called Eulerian numbers as coefficients. In addition, stochastic ordering and moment ordering results for the sojourn time distribution are obtained.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages22
Publication statusPublished - 2005

Publication series

NameMemorandum Faculty of Mathematical Sciences
PublisherUniversity of Twente, Department of Applied Mathematics
No.1766
ISSN (Print)0169-2690

Keywords

  • MSC-60E15
  • EWI-3586
  • METIS-248083
  • IR-65950
  • MSC-60K25

Cite this

Cheung, S. K., van den Berg, H. L., & Boucherie, R. J. (2005). Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue. (Memorandum Faculty of Mathematical Sciences; No. 1766). Enschede: University of Twente, Department of Applied Mathematics.