Two coupled Lévy queues with independent input

O.J. Boxma, J. Ivanovs

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Abstract

We consider a pair of coupled queues driven by independent spectrally-positive Lévy processes. With respect to the bi-variate workload process this framework includes both the coupled processor model and the two-server fluid network with independent Lévy inputs. We identify the joint transform of the stationary workload distribution in terms of Wiener-Hopf factors corresponding to two auxiliary Lévy processes with explicit Laplace exponents. We reinterpret and extend the ideas of Boxma (1983) to provide a general and uniform result with a neat transform expression. Keywords: Coupled processor model, fluid network, Lévy input, Wiener-Hopf factorization.
Original languageEnglish
Pages (from-to)574-590
Number of pages17
JournalStochastic Systems
Volume3
Issue number2
DOIs
Publication statusPublished - 2013

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