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Jackson networks in nonautonomous random environments

Research output: Journal contributions › Journal articles › Research › peer-review

Standard

Jackson networks in nonautonomous random environments. / Krenzler, Ruslan; Daduna, Hans; Otten, Sonja.
In: Advances in Applied Probability, Vol. 48, No. 2, 06.2016, p. 315–331.

Research output: Journal contributions › Journal articles › Research › peer-review

Harvard

Krenzler, R, Daduna, H & Otten, S 2016, 'Jackson networks in nonautonomous random environments', Advances in Applied Probability, vol. 48, no. 2, pp. 315–331. https://doi.org/10.1017/apr.2016.2

APA

Krenzler, R., Daduna, H., & Otten, S. (2016). Jackson networks in nonautonomous random environments. Advances in Applied Probability, 48(2), 315–331. https://doi.org/10.1017/apr.2016.2

Vancouver

Krenzler R, Daduna H, Otten S. Jackson networks in nonautonomous random environments. Advances in Applied Probability. 2016 Jun;48(2):315–331. doi: 10.1017/apr.2016.2

Bibtex

@article{6352f2e540bd407eb40438d35cad4504,
title = "Jackson networks in nonautonomous random environments",
abstract = "We investigate queueing networks in a random environment. The impact of the evolving environment on the network is by changing service capacities (upgrading and/or degrading, breakdown, repair) when the environment changes its state. On the other side, customers departing from the network may enforce the environment to jump immediately. This means that the environment is nonautonomous and therefore results in a rather complex two-way interaction, especially if the environment is not itself Markov. To react to the changes of the capacities we implement randomised versions of the well-known deterministic rerouteing schemes 'skipping' (jump-over protocol) and `reflection' (repeated service, random direction). Our main result is an explicit expression for the joint stationary distribution of the queue-lengths vector and the environment which is of product form. ",
keywords = "Mathematics, Randomised random walks, Jackson network, skipping, processes in random environment, reflection, product form steady state, breakdown of nodes, degrading services, speed-up of service, Informatics, Jackson network, breakdown of nodes",
author = "Ruslan Krenzler and Hans Daduna and Sonja Otten",
year = "2016",
month = jun,
doi = "10.1017/apr.2016.2",
language = "English",
volume = "48",
pages = "315–331",
journal = "Advances in Applied Probability",
issn = "0001-8678",
publisher = "Cambridge University Press",
number = "2",

}

RIS

TY - JOUR

T1 - Jackson networks in nonautonomous random environments

AU - Krenzler, Ruslan

AU - Daduna, Hans

AU - Otten, Sonja

PY - 2016/6

Y1 - 2016/6

N2 - We investigate queueing networks in a random environment. The impact of the evolving environment on the network is by changing service capacities (upgrading and/or degrading, breakdown, repair) when the environment changes its state. On the other side, customers departing from the network may enforce the environment to jump immediately. This means that the environment is nonautonomous and therefore results in a rather complex two-way interaction, especially if the environment is not itself Markov. To react to the changes of the capacities we implement randomised versions of the well-known deterministic rerouteing schemes 'skipping' (jump-over protocol) and `reflection' (repeated service, random direction). Our main result is an explicit expression for the joint stationary distribution of the queue-lengths vector and the environment which is of product form.

AB - We investigate queueing networks in a random environment. The impact of the evolving environment on the network is by changing service capacities (upgrading and/or degrading, breakdown, repair) when the environment changes its state. On the other side, customers departing from the network may enforce the environment to jump immediately. This means that the environment is nonautonomous and therefore results in a rather complex two-way interaction, especially if the environment is not itself Markov. To react to the changes of the capacities we implement randomised versions of the well-known deterministic rerouteing schemes 'skipping' (jump-over protocol) and `reflection' (repeated service, random direction). Our main result is an explicit expression for the joint stationary distribution of the queue-lengths vector and the environment which is of product form.

KW - Mathematics

KW - Randomised random walks

KW - Jackson network

KW - skipping

KW - processes in random environment

KW - reflection

KW - product form steady state

KW - breakdown of nodes

KW - degrading services

KW - speed-up of service

KW - Informatics

KW - Jackson network

KW - breakdown of nodes

UR - http://www.scopus.com/inward/record.url?scp=84976420385&partnerID=8YFLogxK

U2 - 10.1017/apr.2016.2

DO - 10.1017/apr.2016.2

M3 - Journal articles

VL - 48

SP - 315

EP - 331

JO - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - 2

ER -

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Research output: Journal contributions › Journal articles › Research › peer-review

Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems

Otten, S., Krenzler, R., Xie, L., Daduna, H. & Kruse, K., 06.2022, In: OR Spectrum. 44, 2, p. 603-648 46 p.

Research output: Journal contributions › Journal articles › Research › peer-review

Introducing split orders and optimizing operational policies in robotic mobile fulfillment systems

Xie, L., Thieme, N., Krenzler, R. & Li, H., 01.01.2021, In: European Journal of Operational Research . 288, 1, p. 80-97 18 p.

Research output: Journal contributions › Journal articles › Research › peer-review

Performance analysis for loss systems with many subscribers and concurrent services

Daduna, H. & Krenzler, R., 2020, Measurement, Modelling and Evaluation of Computing Systems : 20th International GI/ITG Conference, MMB 2020, Saarbrücken, Germany, March 16–18, 2020, Proceedings. Hermanns, H. (ed.). Cham: Springer Verlag, p. 118-135 18 p. (Lecture Notes in Computer Science ; vol. 12040 LNCS)(Programming and Software Engineering; vol. 12040).

Research output: Contributions to collected editions/works › Article in conference proceedings › Research › peer-review

Efficient Order Picking Methods in Robotic Mobile Fulfillment Systems

Xie, L., Thieme, N., Krenzler, R. & Li, H., 2019, 31 p.

Research output: Working paper › Working papers

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