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 language | English |
---|---|
Pages (from-to) | 293-319 |
Number of pages | 27 |
Journal | Queueing systems |
Volume | 79 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2015 |
Externally published | Yes |