Standard

REGULAR VARIATION IN A FIXED-POINT PROBLEM FOR SINGLE- AND MULTI-CLASS BRANCHING PROCESSES AND QUEUES. / Asmussen, Soren; Foss, Sergey.

In: Advances in Applied Probability, Vol. 50, No. A, 01.12.2018, p. 47-61.

Research output: Contribution to journal › Article › peer-review

Harvard

Asmussen, S & Foss, S 2018, 'REGULAR VARIATION IN A FIXED-POINT PROBLEM FOR SINGLE- AND MULTI-CLASS BRANCHING PROCESSES AND QUEUES', Advances in Applied Probability, vol. 50, no. A, pp. 47-61. https://doi.org/10.1017/apr.2018.69

APA

Asmussen, S., & Foss, S. (2018). REGULAR VARIATION IN A FIXED-POINT PROBLEM FOR SINGLE- AND MULTI-CLASS BRANCHING PROCESSES AND QUEUES. Advances in Applied Probability, 50(A), 47-61. https://doi.org/10.1017/apr.2018.69

Vancouver

Asmussen S, Foss S. REGULAR VARIATION IN A FIXED-POINT PROBLEM FOR SINGLE- AND MULTI-CLASS BRANCHING PROCESSES AND QUEUES. Advances in Applied Probability. 2018 Dec 1;50(A):47-61. doi: 10.1017/apr.2018.69

Author

Asmussen, Soren ; Foss, Sergey. / REGULAR VARIATION IN A FIXED-POINT PROBLEM FOR SINGLE- AND MULTI-CLASS BRANCHING PROCESSES AND QUEUES. In: Advances in Applied Probability. 2018 ; Vol. 50, No. A. pp. 47-61.

BibTeX

@article{89d9eca9fb5649c9a31754ecec06d149,
title = "REGULAR VARIATION IN A FIXED-POINT PROBLEM FOR SINGLE- AND MULTI-CLASS BRANCHING PROCESSES AND QUEUES",
abstract = "Tail asymptotics of the solution R to a fixed-point problem of the type R =(D) Q + Sigma(N)(1) R-m are derived under heavy-tailed conditions allowing both dependence between Q and N and the tails to be of the same order of magnitude. Similar results are derived for a K-class version with applications to multi-type branching processes and busy periods in multi-class queues.",
keywords = "Busy period, Galton-Watson process, intermediate regular variation, multivariate regular variation, random recursion, random sum, ASYMPTOTICS",
author = "Soren Asmussen and Sergey Foss",
year = "2018",
month = dec,
day = "1",
doi = "10.1017/apr.2018.69",
language = "English",
volume = "50",
pages = "47--61",
journal = "Advances in Applied Probability",
issn = "0001-8678",
publisher = "Applied Probability Trust",
number = "A",

}

RIS

TY - JOUR

T1 - REGULAR VARIATION IN A FIXED-POINT PROBLEM FOR SINGLE- AND MULTI-CLASS BRANCHING PROCESSES AND QUEUES

AU - Asmussen, Soren

AU - Foss, Sergey

PY - 2018/12/1

Y1 - 2018/12/1

N2 - Tail asymptotics of the solution R to a fixed-point problem of the type R =(D) Q + Sigma(N)(1) R-m are derived under heavy-tailed conditions allowing both dependence between Q and N and the tails to be of the same order of magnitude. Similar results are derived for a K-class version with applications to multi-type branching processes and busy periods in multi-class queues.

AB - Tail asymptotics of the solution R to a fixed-point problem of the type R =(D) Q + Sigma(N)(1) R-m are derived under heavy-tailed conditions allowing both dependence between Q and N and the tails to be of the same order of magnitude. Similar results are derived for a K-class version with applications to multi-type branching processes and busy periods in multi-class queues.

KW - Busy period

KW - Galton-Watson process

KW - intermediate regular variation

KW - multivariate regular variation

KW - random recursion

KW - random sum

KW - ASYMPTOTICS

UR - http://www.scopus.com/inward/record.url?scp=85055242638&partnerID=8YFLogxK

U2 - 10.1017/apr.2018.69

DO - 10.1017/apr.2018.69

M3 - Article

VL - 50

SP - 47

EP - 61

JO - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - A

ER -

ID: 18631931