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

2017/09/15 by Søren Asmussen, Asmussen, Søren, Sergey Foss +1 · 2 citations
Business, Management and Accounting · Mathematics · #60F10 #60H25 #60J80 #60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1709.05140

openalex publication_date 2017/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Tail asymptotics of the solution R to a fixpoint problem of type R =_st\nQ + \∑₁^N R_m is derived under heavy-tailed conditions allowing both\ndependence between Q and N and the tails to be of the same order of\nmagnitude. Similar results are derived for a K-class version with\napplications to multitype branching processes and busy periods in multiclass\nqueues.\n

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• Heavy-tail asymptotics for the length of a busy period in a Generalised Jackson Network

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