Two coupled Lévy queues with independent input

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