15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Sektion 12 - Wahrscheinlichkeitstheorie, Statistik
Dienstag, 18. September 2001, 17.00, Hörsaal 7


On the Moments of the Overflow and Freed Carried Traffic for the $ GI/M/C/0$ System

Manfred Brandt, Konrad-Zuse-Zentrum für Informationstechnik Berlin (Koautor: Andreas Brandt)


In circuit switching networks call streams are characterized by their mean and peakedness (two-moment method). The $ GI/M/C/0$ system is used to model a single link, where the $ GI$-stream is determined by fitting moments appropriately. For the moments of the overflow traffic of a $ GI/M/C/0$ system there are efficient numerical algorithms available. However, for the moments of the freed carried traffic, defined as the moments of a virtual link of infinite capacity to which the process of calls accepted by the link (carried arrival process) is virtually directed and where the virtual calls get fresh exponential i.i.d. holding times, only complex numerical algorithms are available. This is the reason why the concept of the freed carried traffic is not used rigorously. The main result of this talk is an efficient algorithm for computing the moments of the freed carried traffic, in particular an explicit formula for its peakedness. This result offers a unified handling of both overflow and carried traffics in networks. Furthermore, some refined characteristics for the overflow and freed carried streams are derived.

E-Mail: brandt@zib.de
Homepage: www.zib.de/brandt/

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