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

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10 Citations (Scopus)

51 Downloads (Pure)

Abstract

Tail asymptotics of the solution R to a fixed-point problem of the type R=^DQ+-1^NRm 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 Feb 2019

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Applied Mathematics

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Regular variation in a fixed-point problem for single-and multi-class branching processes and queues

Abstract

Keywords

ASJC Scopus subject areas

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