The problem of stability in queueing theory

S. T. Rachev

doi:10.1007/BF01159470

The problem of stability in queueing theory

S. T. Rachev

Mathematics and Statistics

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Abstract

The stability problem in queueing theory is concerned with the continuity of the mapping F from the set U of the input flows into the set V of the output flows. First, using the theory of probability metrics we estimate the modulus of F-continuity providing that U and V have structures of metric spaces. Then we evaluate the error terms in the approximation of the input flows by simpler ones assuming that we have observed some functionals of the empirical input flows distributions.

Original language	English
Pages (from-to)	287-317
Number of pages	31
Journal	Queueing Systems
Volume	4
Issue number	4
DOIs	https://doi.org/10.1007/BF01159470
State	Published - Dec 1989

Keywords

Stability and continuity of queueing models
moment and marginal problems
probability metrics

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10.1007/BF01159470

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AB - The stability problem in queueing theory is concerned with the continuity of the mapping F from the set U of the input flows into the set V of the output flows. First, using the theory of probability metrics we estimate the modulus of F-continuity providing that U and V have structures of metric spaces. Then we evaluate the error terms in the approximation of the input flows by simpler ones assuming that we have observed some functionals of the empirical input flows distributions.

KW - Stability and continuity of queueing models

KW - moment and marginal problems

KW - probability metrics

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The problem of stability in queueing theory

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Keywords

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