EXTREMAL PROPERTY OF WAITING TIMES IN $GI|G|1|\infty$ MODEL

Authors

  • A. A. Danielyan Chair of the Theory of Probability and Mathematical Statistics, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2005.39.3.047

Keywords:

waiting times, FIFO discipline, Poissonian entering stream

Abstract

In the present paper stationary distribution functions W and W* of waiting times, which are limits for actual and virtual waiting times across the time axis, in the GI|G| 1 |∞ model under FIFO discipline are examined. The following extremal property is proved. For all x ∊(0,+∞) in the case of non-Poissonian entering stream of demands the strict inequalities W(x)>W*(x)> Ŵ(x) are valid, where Ŵ is the waiting times’ stationary distribution function in the case of the Poissonian entering stream.

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Published

2005-10-20

How to Cite

Danielyan, A. A. (2005). EXTREMAL PROPERTY OF WAITING TIMES IN $GI|G|1|\infty$ MODEL. Proceedings of the YSU A: Physical and Mathematical Sciences, 39(3 (208), 47–52. https://doi.org/10.46991/PYSU:A/2005.39.3.047

Issue

Section

Mathematics