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

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

Research output: Book/ReportReportAcademic

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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-traf¿c 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-traf¿c 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 re¿ected Brownian motions in the non-negative orthant.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages22
Publication statusPublished - 2013

Publication series

NameReport Eurandom
Volume2013005
ISSN (Print)1389-2355

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Parallel Queues
Heavy Traffic
Matrix Analytic Methods
Functional Central Limit Theorem
Single Server Queue
Continuous-time Markov Chain
Semimartingale
Queue Length
Limiting Distribution
Waiting Time
Joint Distribution
Workload
Brownian motion
Server
Non-negative

Cite this

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Heavy-traffic asymptotics for networks of parallel queues with Markov-modulated service speeds. / Dorsman, J.L.; Vlasiou, M.; Zwart, B.

Eindhoven : Eurandom, 2013. 22 p. (Report Eurandom; Vol. 2013005).

Research output: Book/ReportReportAcademic

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