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Queueing Systems
Published in: Queueing Systems 1-2/2022

27-09-2022

Large deviations for stochastic fluid networks with Weibullian tails

Authors: Mihail Bazhba, Chang-Han Rhee, Bert Zwart

Published in: Queueing Systems | Issue 1-2/2022

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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 \(J_1\) 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 \(J_1\) topology.
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Appendix
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Metadata
Title
Large deviations for stochastic fluid networks with Weibullian tails
Authors
Mihail Bazhba
Chang-Han Rhee
Bert Zwart
Publication date
27-09-2022
Publisher
Springer US
Published in
Queueing Systems / Issue 1-2/2022
Print ISSN: 0257-0130
Electronic ISSN: 1572-9443
DOI
https://doi.org/10.1007/s11134-022-09865-5

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