Heavy-traffic asymptotics for networks of parallel queues with Markov-modulated service speeds

J.L. Dorsman, M. Vlasiou, B. Zwart

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7 Citations (Scopus)
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Abstract

We study a network of parallel single-server queues, where the speeds of the servers are varying over time and governed by a single continuous-time Markov chain. We obtain heavy-traffic limits for the distributions of the joint workload, waiting-time and queue length processes. We do so by using a functional central limit theorem approach, which requires the interchange of steady-state and heavy-traffic limits. The marginals of these limiting distributions are shown to be exponential with rates that can be computed by matrix-analytic methods. Moreover, we show how to numerically compute the joint distributions, by viewing the limit processes as multi-dimensional semi-martingale reflected Brownian motions in the non-negative orthant. Keywords: Functional central limit theorem; Layered queueing networks; Machine-repair model; Semi-martingale reflected Brownian motion
Original languageEnglish
Pages (from-to)293-319
Number of pages27
JournalQueueing Systems: Theory and Applications
Volume79
Issue number3
DOIs
Publication statusPublished - 2015

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Parallel Queues
Heavy Traffic
Brownian movement
Reflected Brownian Motion
Functional Central Limit Theorem
Servers
Semimartingale
Queueing networks
Interchanges
Matrix Analytic Methods
Markov processes
Single Server Queue
Repair
Continuous-time Markov Chain
Queueing Networks
Queue Length
Limiting Distribution
Waiting Time
Joint Distribution
Workload

Cite this

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abstract = "We study a network of parallel single-server queues, where the speeds of the servers are varying over time and governed by a single continuous-time Markov chain. We obtain heavy-traffic limits for the distributions of the joint workload, waiting-time and queue length processes. We do so by using a functional central limit theorem approach, which requires the interchange of steady-state and heavy-traffic limits. The marginals of these limiting distributions are shown to be exponential with rates that can be computed by matrix-analytic methods. Moreover, we show how to numerically compute the joint distributions, by viewing the limit processes as multi-dimensional semi-martingale reflected Brownian motions in the non-negative orthant. Keywords: Functional central limit theorem; Layered queueing networks; Machine-repair model; Semi-martingale reflected Brownian motion",
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Heavy-traffic asymptotics for networks of parallel queues with Markov-modulated service speeds. / Dorsman, J.L.; Vlasiou, M.; Zwart, B.

In: Queueing Systems: Theory and Applications, Vol. 79, No. 3, 2015, p. 293-319.

Research output: Contribution to journalArticleAcademicpeer-review

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