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- Title
Heavy-traffic asymptotics for networks of parallel queues with Markov-modulated service speeds.
- Authors
Dorsman, Jan-Pieter; Vlasiou, Maria; Zwart, Bert
- 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.
- Subjects
CENTRAL limit theorem; QUEUEING networks; BROWNIAN motion; MARTINGALES (Mathematics); CLIENT/SERVER computing; MARKOV processes; MATRIX analytic methods
- Publication
Queueing Systems, 2015, Vol 79, Issue 3/4, p293
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-014-9422-x