Decomposition and aggregation in queueing networks

Tijs Huisman

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

2 Citations (Scopus)
86 Downloads (Pure)

Abstract

This chapter considers the decomposition and aggregation of multiclass queueing networks with state-dependent routing. Combining state-dependent generalisations of quasi-reversibility and biased local balance, sufficient conditions are obtained under which the stationary distribution of the network is of product-form. This product-formfactorises into one part that describes the nodes of the network in isolation, and one part that describes the routing and the global network state. It is shown that a decomposition holds for general nodes if the input-output behaviour of these nodes is suitably compensated by the state-dependent routing function. When only a subset of the nodes is of interest, it is shown that the other nodes may be aggregated into nodes that only capture their global behaviour. The results both unify and extend existing classes of product-form networks, as is illustrated by several cases and an example of an assembly network.
Original languageUndefined
Title of host publicationQueueing Networks: A Fundamental Approach
EditorsRichardus J. Boucherie, Nico van Dijk, Nico M. van Dijk
Place of PublicationNew York
PublisherSpringer
Pages313-344
Number of pages32
ISBN (Print)978-1-4419-6471-7
DOIs
Publication statusPublished - 2011

Publication series

NameInternational Series in Operations Research & Management Science
PublisherSpringer Science + Business Media
Number154
Volume154
ISSN (Print)0884-8289

Keywords

  • METIS-277442
  • EWI-18751
  • IR-75065

Cite this

Huisman, T. (2011). Decomposition and aggregation in queueing networks. In R. J. Boucherie, N. van Dijk, & N. M. van Dijk (Eds.), Queueing Networks: A Fundamental Approach (pp. 313-344). (International Series in Operations Research & Management Science; Vol. 154, No. 154). New York: Springer. https://doi.org/10.1007/978-1-4419-6472-4_7
Huisman, Tijs. / Decomposition and aggregation in queueing networks. Queueing Networks: A Fundamental Approach. editor / Richardus J. Boucherie ; Nico van Dijk ; Nico M. van Dijk. New York : Springer, 2011. pp. 313-344 (International Series in Operations Research & Management Science; 154).
@inbook{ca5462f7bbd348e3b3f2327f951507c3,
title = "Decomposition and aggregation in queueing networks",
abstract = "This chapter considers the decomposition and aggregation of multiclass queueing networks with state-dependent routing. Combining state-dependent generalisations of quasi-reversibility and biased local balance, sufficient conditions are obtained under which the stationary distribution of the network is of product-form. This product-formfactorises into one part that describes the nodes of the network in isolation, and one part that describes the routing and the global network state. It is shown that a decomposition holds for general nodes if the input-output behaviour of these nodes is suitably compensated by the state-dependent routing function. When only a subset of the nodes is of interest, it is shown that the other nodes may be aggregated into nodes that only capture their global behaviour. The results both unify and extend existing classes of product-form networks, as is illustrated by several cases and an example of an assembly network.",
keywords = "METIS-277442, EWI-18751, IR-75065",
author = "Tijs Huisman",
note = "10.1007/978-1-4419-6472-4_7",
year = "2011",
doi = "10.1007/978-1-4419-6472-4_7",
language = "Undefined",
isbn = "978-1-4419-6471-7",
series = "International Series in Operations Research & Management Science",
publisher = "Springer",
number = "154",
pages = "313--344",
editor = "Boucherie, {Richardus J.} and {van Dijk}, Nico and {van Dijk}, {Nico M.}",
booktitle = "Queueing Networks: A Fundamental Approach",

}

Huisman, T 2011, Decomposition and aggregation in queueing networks. in RJ Boucherie, N van Dijk & NM van Dijk (eds), Queueing Networks: A Fundamental Approach. International Series in Operations Research & Management Science, no. 154, vol. 154, Springer, New York, pp. 313-344. https://doi.org/10.1007/978-1-4419-6472-4_7

Decomposition and aggregation in queueing networks. / Huisman, Tijs.

Queueing Networks: A Fundamental Approach. ed. / Richardus J. Boucherie; Nico van Dijk; Nico M. van Dijk. New York : Springer, 2011. p. 313-344 (International Series in Operations Research & Management Science; Vol. 154, No. 154).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

TY - CHAP

T1 - Decomposition and aggregation in queueing networks

AU - Huisman, Tijs

N1 - 10.1007/978-1-4419-6472-4_7

PY - 2011

Y1 - 2011

N2 - This chapter considers the decomposition and aggregation of multiclass queueing networks with state-dependent routing. Combining state-dependent generalisations of quasi-reversibility and biased local balance, sufficient conditions are obtained under which the stationary distribution of the network is of product-form. This product-formfactorises into one part that describes the nodes of the network in isolation, and one part that describes the routing and the global network state. It is shown that a decomposition holds for general nodes if the input-output behaviour of these nodes is suitably compensated by the state-dependent routing function. When only a subset of the nodes is of interest, it is shown that the other nodes may be aggregated into nodes that only capture their global behaviour. The results both unify and extend existing classes of product-form networks, as is illustrated by several cases and an example of an assembly network.

AB - This chapter considers the decomposition and aggregation of multiclass queueing networks with state-dependent routing. Combining state-dependent generalisations of quasi-reversibility and biased local balance, sufficient conditions are obtained under which the stationary distribution of the network is of product-form. This product-formfactorises into one part that describes the nodes of the network in isolation, and one part that describes the routing and the global network state. It is shown that a decomposition holds for general nodes if the input-output behaviour of these nodes is suitably compensated by the state-dependent routing function. When only a subset of the nodes is of interest, it is shown that the other nodes may be aggregated into nodes that only capture their global behaviour. The results both unify and extend existing classes of product-form networks, as is illustrated by several cases and an example of an assembly network.

KW - METIS-277442

KW - EWI-18751

KW - IR-75065

U2 - 10.1007/978-1-4419-6472-4_7

DO - 10.1007/978-1-4419-6472-4_7

M3 - Chapter

SN - 978-1-4419-6471-7

T3 - International Series in Operations Research & Management Science

SP - 313

EP - 344

BT - Queueing Networks: A Fundamental Approach

A2 - Boucherie, Richardus J.

A2 - van Dijk, Nico

A2 - van Dijk, Nico M.

PB - Springer

CY - New York

ER -

Huisman T. Decomposition and aggregation in queueing networks. In Boucherie RJ, van Dijk N, van Dijk NM, editors, Queueing Networks: A Fundamental Approach. New York: Springer. 2011. p. 313-344. (International Series in Operations Research & Management Science; 154). https://doi.org/10.1007/978-1-4419-6472-4_7