A Tandem Queue With LÉVY Input: A New Representation Of The Downstream Queue Length
PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES（2007）
摘要
In this article we present a new representation for the steady-state distribution of the workload of the second queue in a two-node tandem network. It involves the difference of two suprema over two adjacent intervals. In the case of spectrally positive Lévy input, this enables us to derive the Laplace transform and Pollaczek–Khintchine representation of the workload of the second queue. Additionally, we obtain the exact distribution of the workload in the case of Brownian and Poisson input, as well as some insightful formulas representing the exact asymptotics for &agr;-stable Lévy inputs.
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关键词
vy input,khintchine representation,large-buffer asymptotics ñ stationary independent increments ñ tandem networks ñ laplace transform ñ l·,downstream queue length,poisson input,spectrally positive l,adjacent interval,exact distribution,tandem queue,exact asymptotics,stable l,new representation,steady-state distribution,laplace transform,steady state
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