Parallel queueing networks with Markov-modulated service speeds in heavy traffic

Jan-Pieter L. Dorsman; Maria Vlasiou; Bert Zwart

doi:10.1145/2518025.2518034

Parallel queueing networks with Markov-modulated service speeds in heavy traffic

Jan-Pieter L. Dorsman, Maria Vlasiou, Bert Zwart

Research output: Contribution to journal › Conference article › Academic › peer-review

3 Citations (Scopus)

2 Downloads (Pure)

Abstract

We study a network of parallel single-server queues, where the service speeds are governed by a continuous-time Markov chain. This generic model finds applications in many areas such as communication systems, computer systems and manufacturing systems. We obtain heavy-traffic approximations for the joint workload, delay and queue length processes by combining a functional central limit theorem approach with matrix-analytic methods. In addition, we numerically compute the joint distributions by viewing the limit processes as semi-martingale reflected Brownian motions.

Original language	English
Pages (from-to)	47-49
Number of pages	3
Journal	SIGMETRICS performance evaluation review
Volume	41
Issue number	2
DOIs	https://doi.org/10.1145/2518025.2518034
Publication status	Published - 2013
Externally published	Yes
Event	IFIP WG 7.3 Performance 2013 31st International Symposium on Computer Performance, Modeling, Measurements and Evaluation, IFIPWG 7.3 Performance 2013 - Vienna, Austria Duration: 24 Sept 2013 → 26 Sept 2013 Conference number: 31

Access to Document

10.1145/2518025.2518034

Cite this

@article{cd7b08e995394697902803827aa24f3d,

title = "Parallel queueing networks with Markov-modulated service speeds in heavy traffic",

abstract = "We study a network of parallel single-server queues, where the service speeds are governed by a continuous-time Markov chain. This generic model finds applications in many areas such as communication systems, computer systems and manufacturing systems. We obtain heavy-traffic approximations for the joint workload, delay and queue length processes by combining a functional central limit theorem approach with matrix-analytic methods. In addition, we numerically compute the joint distributions by viewing the limit processes as semi-martingale reflected Brownian motions.",

author = "Dorsman, {Jan-Pieter L.} and Maria Vlasiou and Bert Zwart",

year = "2013",

doi = "10.1145/2518025.2518034",

language = "English",

volume = "41",

pages = "47--49",

journal = "SIGMETRICS performance evaluation review",

issn = "0163-5999",

publisher = "Association for Computing Machinery",

number = "2",

note = "IFIP WG 7.3 Performance 2013 31st International Symposium on Computer Performance, Modeling, Measurements and Evaluation, IFIPWG 7.3 Performance 2013, IFIPWG 7.3 Performance ; Conference date: 24-09-2013 Through 26-09-2013",

}

TY - JOUR

T1 - Parallel queueing networks with Markov-modulated service speeds in heavy traffic

AU - Dorsman, Jan-Pieter L.

AU - Vlasiou, Maria

AU - Zwart, Bert

N1 - Conference code: 31

PY - 2013

Y1 - 2013

N2 - We study a network of parallel single-server queues, where the service speeds are governed by a continuous-time Markov chain. This generic model finds applications in many areas such as communication systems, computer systems and manufacturing systems. We obtain heavy-traffic approximations for the joint workload, delay and queue length processes by combining a functional central limit theorem approach with matrix-analytic methods. In addition, we numerically compute the joint distributions by viewing the limit processes as semi-martingale reflected Brownian motions.

AB - We study a network of parallel single-server queues, where the service speeds are governed by a continuous-time Markov chain. This generic model finds applications in many areas such as communication systems, computer systems and manufacturing systems. We obtain heavy-traffic approximations for the joint workload, delay and queue length processes by combining a functional central limit theorem approach with matrix-analytic methods. In addition, we numerically compute the joint distributions by viewing the limit processes as semi-martingale reflected Brownian motions.

U2 - 10.1145/2518025.2518034

DO - 10.1145/2518025.2518034

M3 - Conference article

SN - 0163-5999

VL - 41

SP - 47

EP - 49

JO - SIGMETRICS performance evaluation review

JF - SIGMETRICS performance evaluation review

IS - 2

T2 - IFIP WG 7.3 Performance 2013 31st International Symposium on Computer Performance, Modeling, Measurements and Evaluation, IFIPWG 7.3 Performance 2013

Y2 - 24 September 2013 through 26 September 2013

ER -

Parallel queueing networks with Markov-modulated service speeds in heavy traffic

Abstract

Access to Document

Fingerprint

Cite this