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

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

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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
Publication statusPublished - 2013
Externally publishedYes

Publication series

NameEurandom preprint series
No.2013-005

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