Diffusion parameters of flows in stable multi-class queueing networks

Sarat Babu Moka; Yoni Nazarathy; Werner Scheinhardt

doi:10.1007/s11134-022-09869-1

Diffusion parameters of flows in stable multi-class queueing networks

Sarat Babu Moka^*, Yoni Nazarathy, Werner Scheinhardt

^*Corresponding author for this work

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Abstract

We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes the system stable. We study the variability of flows within the network. Computable expressions for quantifying flow variability have previously been discussed in the literature. However, in this paper, we shed more light on such analysis to justify the use of these expressions in the asymptotic analysis of network flows. Toward that end, we find a simple diffusion limit for the inter-class flows and establish the relation to asymptotic (co-)variance rates.

Original language	English
Pages (from-to)	313-346
Number of pages	34
Journal	Queueing systems
Volume	103
Issue number	April 2023
Early online date	24 Nov 2022
DOIs	https://doi.org/10.1007/s11134-022-09869-1
Publication status	Published - 1 Apr 2023

Keywords

2023 OA procedure
Diffusion limits
Asymptotic variance
Queueing networks

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10.1007/s11134-022-09869-1

s11134-022-09869-1Final published version, 578 KBLicence: Taverne

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title = "Diffusion parameters of flows in stable multi-class queueing networks",

abstract = "We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes the system stable. We study the variability of flows within the network. Computable expressions for quantifying flow variability have previously been discussed in the literature. However, in this paper, we shed more light on such analysis to justify the use of these expressions in the asymptotic analysis of network flows. Toward that end, we find a simple diffusion limit for the inter-class flows and establish the relation to asymptotic (co-)variance rates.",

keywords = "2023 OA procedure, Diffusion limits, Asymptotic variance, Queueing networks",

author = "Moka, \{Sarat Babu\} and Yoni Nazarathy and Werner Scheinhardt",

note = "Funding Information: YN is supported by Australian Research Council (ARC) grant DP180101602. Part of the work was carried out, while WS was supported by an Ethel Raybould Visiting Fellowship to the University of Queensland. SBM is supported by the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) under grant number CE140100049. We thank an anonymous referee of this paper for their valuable comments and suggestions, particularly for highlighting the need for Assumption (A7). We also thank an anonymous referee of an earlier version of the paper for drawing our attention to the usefulness of the innovations method calculations. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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doi = "10.1007/s11134-022-09869-1",

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T1 - Diffusion parameters of flows in stable multi-class queueing networks

AU - Moka, Sarat Babu

AU - Nazarathy, Yoni

AU - Scheinhardt, Werner

N1 - Funding Information: YN is supported by Australian Research Council (ARC) grant DP180101602. Part of the work was carried out, while WS was supported by an Ethel Raybould Visiting Fellowship to the University of Queensland. SBM is supported by the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) under grant number CE140100049. We thank an anonymous referee of this paper for their valuable comments and suggestions, particularly for highlighting the need for Assumption (A7). We also thank an anonymous referee of an earlier version of the paper for drawing our attention to the usefulness of the innovations method calculations. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2023/4/1

Y1 - 2023/4/1

N2 - We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes the system stable. We study the variability of flows within the network. Computable expressions for quantifying flow variability have previously been discussed in the literature. However, in this paper, we shed more light on such analysis to justify the use of these expressions in the asymptotic analysis of network flows. Toward that end, we find a simple diffusion limit for the inter-class flows and establish the relation to asymptotic (co-)variance rates.

AB - We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes the system stable. We study the variability of flows within the network. Computable expressions for quantifying flow variability have previously been discussed in the literature. However, in this paper, we shed more light on such analysis to justify the use of these expressions in the asymptotic analysis of network flows. Toward that end, we find a simple diffusion limit for the inter-class flows and establish the relation to asymptotic (co-)variance rates.

KW - 2023 OA procedure

KW - Diffusion limits

KW - Asymptotic variance

KW - Queueing networks

U2 - 10.1007/s11134-022-09869-1

DO - 10.1007/s11134-022-09869-1

M3 - Article

SN - 0257-0130

VL - 103

SP - 313

EP - 346

JO - Queueing systems

JF - Queueing systems

IS - April 2023

ER -

Diffusion parameters of flows in stable multi-class queueing networks

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