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

Soren Asmussen, Sergey Foss

Research output: Contribution to journalArticle

2 Citations (Scopus)
7 Downloads (Pure)

Abstract

Tail asymptotics of the solution R to a fixed-point problem of the type R=DQ+-1NRm 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 languageEnglish
Pages (from-to)47-61
Number of pages15
JournalAdvances in Applied Probability
Volume50
Issue numberA
DOIs
Publication statusPublished - 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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