Simple approximations for the gi/g/c queue—ii: The moments, the inverse distribution function and the loss function of the number in the system and of the queue delay

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Abstract

Based on results obtained in part I of this paper, approximations for the first four moments of the number in the system are developed and thence used to approximate the inverse distribution function (IDF) and the loss functions (LF), employing Shore’s general approximations. Existing approximations for the first two moments of queueing time in a GI/G/1 queue serve to approximate the IDF and the LF of queueing time in the corresponding GI/G/c queue. The accuracy attained is generally satisfactory, while a remarkable algebraic simplicity is preserved. A numerical example demonstrates the applicability of some of the new approximations to solve optimization problems.

Original languageEnglish
Pages (from-to)381-391
Number of pages11
JournalJournal of the Operational Research Society
Volume39
Issue number4
DOIs
StatePublished - 1 Jan 1988
Externally publishedYes

Keywords

  • Approximations
  • Inverse distribution function
  • Loss function
  • Moments
  • Queueing
  • Waiting time

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