an:06318823
Zbl 1296.60241
Boxma, Onno; Ivanovs, Jevgenijs
Two coupled L??vy queues with independent input
EN
Stoch. Syst. 3, No. 2, 574-590 (2013).
00334557
2013
j
60K25 68M20
coupled processor model; fluid network; L??vy input; Wiener-Hopf factorization
Summary: We consider a pair of coupled queues driven by independent spectrally-positive L??vy 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 L??vy inputs. We identify the joint transform of the stationary workload distribution in terms of Wiener-Hopf factors corresponding to two auxiliary L??vy processes with explicit Laplace exponents. We reinterpret and extend the ideas of \textit{J. W. Cohen} and \textit{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.
Zbl 0515.60092