Large deviations for stochastic fluid networks with Weibullian tails

Mihail Bazhba, Chang Han Rhee*, Bert Zwart

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a stochastic fluid network where the external input processes are compound Poisson with heavy-tailed Weibullian jumps. Our results comprise of large deviations estimates for the buffer content process in the vector-valued Skorokhod space which is endowed with the product J1 topology. To illustrate our framework, we provide explicit results for a tandem queue. At the heart of our proof is a recent sample-path large deviations result, and a novel continuity result for the Skorokhod reflection map in the product J1 topology.

Original languageEnglish (US)
Pages (from-to)25-52
Number of pages28
JournalQueueing Systems
Volume102
Issue number1-2
DOIs
StatePublished - Oct 2022

Keywords

  • Fluid networks
  • Heavy tails
  • Large deviations
  • Skorokhod map

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics

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