Continuity of queueing systems with refusals

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Abstract

This paper considers queueing systems of the type G |G|m| 0. The sequence y= {Yn, n=0,1,2,...} is introduced, where Yn is the number of busy apparatuses at the moment of call number n; this sequence is related by rule (1) in the paper to the determining sequence X={Xn, n=0,1,2,...}. Also introduced are the respective sets {Mathematical expression}={x} and y ={y}. This paper uses a method of V. M. Zolotarev to study the continuity of the associated map F: {Mathematical expression}→Y with the help of selected metrics on {Mathematical expression} and y, and constructs quantitative estimates of general type, and also in concrete cases. It is shown that as m→∞, the estimates are transformed into the respective estimates in [2], which are related to the case G|G|∞.

Original languageEnglish
Pages (from-to)2307-2320
Number of pages14
JournalJournal of Soviet Mathematics
Volume17
Issue number6
DOIs
Publication statusPublished - Dec 1981

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Queueing System
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Continuity of queueing systems with refusals. / Szeidl, L.

In: Journal of Soviet Mathematics, Vol. 17, No. 6, 12.1981, p. 2307-2320.

Research output: Contribution to journalArticle

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