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On the distribution of the number of packets in the fluid flow approximation of packet arrival streams

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Abstract

Fluid flow approximations are widely used for approximating models of communication systems where packet arrival streams are generated in a regular manner over certain intervals (constant rate). The appropriate mathematical model for describing those bursty arrival streams in the fluid flow framework are the well-known Markov modulated rate processes (MMRP). The paper deals with the distribution of the numberN(t) of packets in the interval [0,t] of MMRP. For two-state MMRPs and their superpositions we derive formulas for the distribution ofN(t) and its density. Further we give asymptotic results. The presented numerical results and simulation studies illustrate the goodness of the fluid flow approximation and show that the proposed numerical algorithms work well even in the case of multiplexing a large number of burst silence sources.

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Authors and Affiliations

  1. FB Wirtschaftswissenschaften, Humboldt-Universität, Spandauer Strage 1, D-10178, Berlin, Germany

    Andreas Brandt

  2. FB Mathematik, Humboldt-Universität, Unter den Linden 6, D-10099, Berlin, Germany

    Manfred Brandt

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  1. Andreas Brandt
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  2. Manfred Brandt
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This work was partially supported by a grant from the Deutsche Bundespost TELEKOM.

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Brandt, A., Brandt, M. On the distribution of the number of packets in the fluid flow approximation of packet arrival streams. Queueing Syst 17, 275–315 (1994). https://doi.org/10.1007/BF01158697

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  • DOI: https://doi.org/10.1007/BF01158697

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