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A TANDEM QUEUE WITH LÉVY INPUT: A NEW REPRESENTATION OF THE DOWNSTREAM QUEUE LENGTH

Published online by Cambridge University Press:  15 December 2006

Krzysztof Debicki ,
Michel Mandjes  and
Miranda van Uitert
Krzysztof Debicki
Affiliation:
Mathematical Institute, University of Wrocław, 50-384 Wrocław, Poland, E-mail: [email protected]
Michel Mandjes
Affiliation:
CWI, 1090 GB Amsterdam, The Netherlands, Korteweg-de Vries Institute, University of Amsterdam, 1018 TV Amsterdam, The Netherlands, and, EURANDOM, 5600 MB Eindhoven, The Netherlands, E-mail: [email protected]
Miranda van Uitert
Affiliation:
The Netherlands Cancer Institute, 1066 CX Amsterdam, The Netherlands, and Information and Communication Theory Group, Delft University of Technology, 2600 GA Delft, The Netherlands, E-mail: [email protected]
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Abstract

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 α-stable Lévy inputs.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 1 , January 2007 , pp. 83 - 107
Copyright
© 2007 Cambridge University Press

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