Stochastic Systems

Two coupled Lévy queues with independent input

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

Article information

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

Dates
First available in Project Euclid: 11 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.ssy/1392131424

Digital Object Identifier
doi:10.1214/13-SSY116

Mathematical Reviews number (MathSciNet)
MR3353211

Zentralblatt MATH identifier
1296.60241

Keywords
Coupled processor model fluid network Lévy input Wiener-Hopf factorization

Citation

Boxma, Onno; Ivanovs, Jevgenijs. Two coupled Lévy queues with independent input. Stoch. Syst. 3 (2013), no. 2, 574--590. doi:10.1214/13-SSY116. https://projecteuclid.org/euclid.ssy/1392131424


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