THE REGULARITIES OF QUEUES IN MODELS WITH INFINITE WAITING ROOM

Authors

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

DOI:

https://doi.org/10.46991/PYSU:A/2006.40.2.003

Keywords:

Queueing Theory, $GI|G|s|\infty$ model, fixed and heavy traffic conditions

Abstract

In the present paper the developments of Queueing Theory is described, its belongness to Operations Research and Probability Theory is substantiated. The Regularities of Many Servers Queues with infinite waiting room are explained on the example of $GI|G|s|\infty$ model. The explicit formulas, limit theorems in c, stability, inequalities for the main characteristics, extremal problems are presented. The main attention in future is given to $GI|G|s|\infty$ model with FIFO service discipline. Not only known results are formulated, but also some results, which were established by authors. For instance, in $GI|G|s|\infty$ model two groups of assumptions are suggested, which lead to the Little formulas. In particular, $M|G|s|\infty$ model is considered.

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Published

2006-05-30

How to Cite

Danielyan, E. A., Danielyan, A. A., & Danielyan, I. E. (2006). THE REGULARITIES OF QUEUES IN MODELS WITH INFINITE WAITING ROOM. Proceedings of the YSU A: Physical and Mathematical Sciences, 40(2 (210), 3–24. https://doi.org/10.46991/PYSU:A/2006.40.2.003

Issue

Section

Mathematics