Large deviations for stochastic fluid networks with Weibullian tails

Mihail Bazhba; Chang Han Rhee; Bert Zwart

doi:10.1007/s11134-022-09865-5

Large deviations for stochastic fluid networks with Weibullian tails

Mihail Bazhba, Chang Han Rhee^*, Bert Zwart

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	25-52
Number of pages	28
Journal	Queueing Systems
Volume	102
Issue number	1-2
DOIs	https://doi.org/10.1007/s11134-022-09865-5
State	Published - Oct 2022

Funding

The research of MB is supported by NWO-Vici grant 2020-25. The research of C-HR is supported by NSF Grant CMMI-2146530. The authors are grateful to Kavita Ramanan for insightful comments regarding the continuity of the reflection map.

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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title = "Large deviations for stochastic fluid networks with Weibullian tails",

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.",

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author = "Mihail Bazhba and Rhee, {Chang Han} and Bert Zwart",

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T1 - Large deviations for stochastic fluid networks with Weibullian tails

AU - Bazhba, Mihail

AU - Rhee, Chang Han

AU - Zwart, Bert

PY - 2022/10

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N2 - 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.

AB - 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.

KW - Fluid networks

KW - Heavy tails

KW - Large deviations

KW - Skorokhod map

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ER -

Large deviations for stochastic fluid networks with Weibullian tails

Abstract

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Keywords

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