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

Please always quote using this URN: urn:nbn:de:0297-zib-6355
  • 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 paper 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.

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Metadaten
Author:Andreas Brandt, Manfred Brandt
Document Type:ZIB-Report
Tag:GI/M/C/0 system; carried arrival process; difference; factorial moments; freed carried traffic; overflow traffic; peakedness; two-moment method
MSC-Classification:39-XX DIFFERENCE AND FUNCTIONAL EQUATIONS / 39Axx Difference equations (For dynamical systems, see 37-XX, for dynamic equations on time scales, see 34N05) / 39A10 Difference equations, additive
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G10 Stationary processes
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Kxx Special processes / 60K25 Queueing theory [See also 68M20, 90B22]
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Mxx Computer system organization / 68M20 Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]
Date of first Publication:2001/05/17
Series (Serial Number):ZIB-Report (01-09)
Published in:Appeared in: Methodology and Computing in Applied Probability 4 (2002) 69-82