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

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...

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Bibliographic Details
Published in:Advances in applied probability 2018-12, Vol.50 (A), p.47-61
Main Authors: Asmussen, Søren, Foss, Sergey
Format: Article
Language:English
Subjects:
Asymptotic methods
Dependence
Fixed points (mathematics)
Mathematical analysis
Original Article
Probability
Queues
Queuing theory
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Summary: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.
ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2018.69