### Abstract

This paper considers queueing systems of the type G |G|m| 0. The sequence y= {Y_{n}, n=0,1,2,...} is introduced, where Y_{n} 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={X_{n}, 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 language | English |
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Pages (from-to) | 2307-2320 |

Number of pages | 14 |

Journal | Journal of Soviet Mathematics |

Volume | 17 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 1981 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Soviet Mathematics*,

*17*(6), 2307-2320. https://doi.org/10.1007/BF01085928

**Continuity of queueing systems with refusals.** / Szeidl, L.

Research output: Contribution to journal › Article

*Journal of Soviet Mathematics*, vol. 17, no. 6, pp. 2307-2320. https://doi.org/10.1007/BF01085928

}

TY - JOUR

T1 - Continuity of queueing systems with refusals

AU - Szeidl, L.

PY - 1981/12

Y1 - 1981/12

N2 - 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|∞.

AB - 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|∞.

UR - http://www.scopus.com/inward/record.url?scp=34250248254&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250248254&partnerID=8YFLogxK

U2 - 10.1007/BF01085928

DO - 10.1007/BF01085928

M3 - Article

AN - SCOPUS:34250248254

VL - 17

SP - 2307

EP - 2320

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -