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

Soren Asmussen, Sergey Foss

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)47-61
Number of pages15
JournalAdvances in Applied Probability
Volume50
Issue numberA
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

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

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