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Two coupled Lévy queues with independent input. (English) Zbl 1296.60241
Summary: 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 J. W. Cohen and O. J. Boxma [Boundary value problems in queueing system analysis. Amsterdam-New York-Oxford: North-Holland Publishing Company (1983; Zbl 0515.60092)] to provide a general and uniform result with a neat transform expression.

MSC:
60K25 Queueing theory (aspects of probability theory)
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
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