, Volume 4, Issue 4, pp 287-317

The problem of stability in queueing theory

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The stability problem in queueing theory is concerned with the continuity of the mappingF from the setU of the input flows into the setV of the output flows. First, using the theory of probability metrics we estimate the modulus ofF-continuity providing thatU andV 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.

Research initiated under support by Army Office of Scientific Research through Mathematical Sciences Institute during the author's visit to MSI in December 1988. References