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Stochastic decompositions in bivariate risk and queueing models with mutual assistance

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Stochastic decompositions in bivariate risk and queueing models with mutual assistance. / Ivanovs, Jevgenijs.

I: Stochastic Models, Bind 37, Nr. 1, 2021, s. 5-22.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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Ivanovs J. Stochastic decompositions in bivariate risk and queueing models with mutual assistance. Stochastic Models. 2021;37(1):5-22. doi: 10.1080/15326349.2020.1760888

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Bibtex

@article{9162f4d5b11f46adbe78f972d4e3cd72,
title = "Stochastic decompositions in bivariate risk and queueing models with mutual assistance",
abstract = "We consider two bivariate models with two-way interactions in context of risk and queueing theory. The two entities interact with each other by providing assistance but otherwise evolve independently. We focus on certain random quantities underlying the joint survival probability and the joint stationary workload, and show that these admit stochastic decomposition. Each one can be seen as an independent sum of respective quantities for the two models with one-way interaction. Additionally, we discuss a rather general method of establishing decompositions from a given kernel equation by identifying two independent random variables from their difference, which may be useful for other models. Finally, we point out that the same decomposition is true for uncorrelated Brownian motion reflected to stay in a quadrant, and it concerns the face measures appearing in the basic adjoint relationship.",
keywords = "basic adjoint relationship, coupled processor, fluid network, kernel equation, reflection in quadrant, stochastic decomposition, two-way interaction",
author = "Jevgenijs Ivanovs",
year = "2021",
doi = "10.1080/15326349.2020.1760888",
language = "English",
volume = "37",
pages = "5--22",
journal = "Stochastic Models",
issn = "1532-6349",
publisher = "Taylor & Francis Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - Stochastic decompositions in bivariate risk and queueing models with mutual assistance

AU - Ivanovs, Jevgenijs

PY - 2021

Y1 - 2021

N2 - We consider two bivariate models with two-way interactions in context of risk and queueing theory. The two entities interact with each other by providing assistance but otherwise evolve independently. We focus on certain random quantities underlying the joint survival probability and the joint stationary workload, and show that these admit stochastic decomposition. Each one can be seen as an independent sum of respective quantities for the two models with one-way interaction. Additionally, we discuss a rather general method of establishing decompositions from a given kernel equation by identifying two independent random variables from their difference, which may be useful for other models. Finally, we point out that the same decomposition is true for uncorrelated Brownian motion reflected to stay in a quadrant, and it concerns the face measures appearing in the basic adjoint relationship.

AB - We consider two bivariate models with two-way interactions in context of risk and queueing theory. The two entities interact with each other by providing assistance but otherwise evolve independently. We focus on certain random quantities underlying the joint survival probability and the joint stationary workload, and show that these admit stochastic decomposition. Each one can be seen as an independent sum of respective quantities for the two models with one-way interaction. Additionally, we discuss a rather general method of establishing decompositions from a given kernel equation by identifying two independent random variables from their difference, which may be useful for other models. Finally, we point out that the same decomposition is true for uncorrelated Brownian motion reflected to stay in a quadrant, and it concerns the face measures appearing in the basic adjoint relationship.

KW - basic adjoint relationship

KW - coupled processor

KW - fluid network

KW - kernel equation

KW - reflection in quadrant

KW - stochastic decomposition

KW - two-way interaction

UR - http://www.scopus.com/inward/record.url?scp=85085003578&partnerID=8YFLogxK

U2 - 10.1080/15326349.2020.1760888

DO - 10.1080/15326349.2020.1760888

M3 - Journal article

AN - SCOPUS:85085003578

VL - 37

SP - 5

EP - 22

JO - Stochastic Models

JF - Stochastic Models

SN - 1532-6349

IS - 1

ER -