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

S.K. Cheung (Editor), S.K. Cheung (Editor), Hans Leo van den Berg, Richardus J. Boucherie

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11 Citations (Scopus)
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Abstract

This paper studies the M/G/1 processor-sharing (PS) queue, in particular 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 suitable for computational purposes. This paper derives readily applicable insensitive bounds for all moments of the conditional sojourn time distribution. The instantaneous sojourn time, i.e., the sojourn time of an infinitesimally small job, leads to insensitive upper bounds requiring only knowledge of the traffic intensity and the initial job size. Interestingly, the upper bounds involve polynomials with so-called Eulerian numbers as coefficients. In addition, stochastic ordering and moment ordering results for the sojourn time distribution are obtained. (Keywords: M/G/1 PS - Conditional sojourn time - Moments - Insensitive bounds - Instantaneous sojourn time - Euler's number triangle - Moment ordering - Permanent customers)
Original languageUndefined
Article number10.1007/s11134-006-7583-y
Pages (from-to)7-18
Number of pages12
JournalQueueing systems
Volume53
Issue number1-2
DOIs
Publication statusPublished - Jun 2006

Keywords

  • EWI-1924
  • M/G/1 PS · Conditional sojourn time · Moments · Insensitive bounds · Instantaneous sojourn time · Euler’s number triangle · Moment ordering · Permanent customers
  • METIS-237994
  • IR-62864

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