Regular Variation in a Fixed-Point Problem for Single- and Multiclass Branching Processes and Queues

Abstract

Tail asymptotics of the solution $R$ to a fixpoint problem of type $R{=}_{st}Q+{\sum }_1^N{R}_m$ is 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 multitype branching processes and busy periods in multiclass queues.

19 pages, 1 figure