Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 293-319 |
| Number of pages | 27 |
| Journal | Queueing Systems: Theory and Applications |
| Volume | 79 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2015 |
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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 journal › Article › Academic › peer-review
TY - JOUR
T1 - Heavy-traffic asymptotics for networks of parallel queues with Markov-modulated service speeds
AU - Dorsman, J.L.
AU - Vlasiou, M.
AU - Zwart, B.
PY - 2015
Y1 - 2015
N2 - 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
AB - 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
U2 - 10.1007/s11134-014-9422-x
DO - 10.1007/s11134-014-9422-x
M3 - Article
VL - 79
SP - 293
EP - 319
JO - Queueing Systems: Theory and Applications
JF - Queueing Systems: Theory and Applications
SN - 0257-0130
IS - 3
ER -