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 language | English |
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Place of Publication | Eindhoven |
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Publisher | EURANDOM |
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Publication status | Published - 2013 |
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Externally published | Yes |
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Name | Eurandom preprint series |
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No. | 2013-005 |
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