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

Soren Asmussen; Sergey Foss

doi:10.1017/apr.2018.69

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

Soren Asmussen, Sergey Foss

Applied Probability Laboratory

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

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	47-61
Number of pages	15
Journal	Advances in Applied Probability
Volume	50
Issue number	A
DOIs	https://doi.org/10.1017/apr.2018.69
Publication status	Published - 1 Dec 2018

Keywords

Busy period
Galton-Watson process
intermediate regular variation
multivariate regular variation
random recursion
random sum
ASYMPTOTICS

Access to Document

10.1017/apr.2018.69

Link to publication in Scopus

Cite this

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