Stochastic Systems

Two coupled Lévy queues with independent input

Onno Boxma and Jevgenijs Ivanovs

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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 Cohen and Boxma (1983) to provide a general and uniform result with a neat transform expression.

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Stoch. Syst., Volume 3, Number 2 (2013), 574-590.

First available in Project Euclid: 11 February 2014

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Coupled processor model fluid network Lévy input Wiener-Hopf factorization


Boxma, Onno; Ivanovs, Jevgenijs. Two coupled Lévy queues with independent input. Stoch. Syst. 3 (2013), no. 2, 574--590. doi:10.1214/13-SSY116.

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