Large deviations for stochastic fluid networks with Weibullian tails

Mihail Bazhba (), Chang-Han Rhee () and Bert Zwart ()
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Mihail Bazhba: UvA
Chang-Han Rhee: Northwestern University
Bert Zwart: Centrum Wiskunde Informatica

Queueing Systems: Theory and Applications, 2022, vol. 102, issue 1, No 3, 25-52

Abstract: 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 $$J_1$$ 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 $$J_1$$ J 1 topology.

Keywords: Fluid networks; Large deviations; Skorokhod map; Heavy tails; 60K25; 60F10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11134-022-09865-5

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