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

Author

Listed:
  • Andreas Brandt

    (Humboldt-Universität zu Berlin)

  • Manfred Brandt

    (Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB))

Abstract

In circuit-switched 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. The main result of this paper is a numerically stable and efficient algorithm for computing the moments of 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.

Suggested Citation

  • Andreas Brandt & Manfred Brandt, 2002. "On the Moments of Overflow and Freed Carried Traffic for the GI/M/C/0 System," Methodology and Computing in Applied Probability, Springer, vol. 4(1), pages 69-82, March.
    • Handle: RePEc:spr:metcap:v:4:y:2002:i:1:d:10.1023_a:1015757414583
    DOI: 10.1023/A:1015757414583
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