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Flow-Level Packet Loss Analysis of a Markovian Bottleneck Buffer

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Seminal Contributions to Modelling and Simulation

Part of the book series: Simulation Foundations, Methods and Applications ((SFMA))

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Abstract

Buffer overflow in intermediate network routers is the prime cause of packet loss in wired communication networks. Packet loss is usually quantified by the packet loss ratio , the fraction of packets that are lost in a buffer. While this measure captures part of the loss performance of the buffer, we show that it is insufficient to quantify the effect of loss on user-perceived quality of service for multimedia streaming applications. In this contribution, we refine the quantification of loss in two ways. First, we focus on loss of a single flow, rather than loss in a buffer. Second, we focus on the different moments of the time and number of accepted packets between losses, rather than just the mean number of accepted packets between losses (which directly relates to the packet loss ratio). The network node is modelled as a Markov-modulated M/M/1/N-type queueing system which is sufficiently versatile to capture the arrival correlation while keeping the analysis tractable. We illustrate our approach by some numerical examples.

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Notes

  1. 1.

    Finding the \( N \times M \) matrix \( X \) in \( AX = B \) (A is an \( N \times N \) matrix and B is an \( N \times M \) matrix) by Gaussian elimination requires \( \frac{1}{3}N^{3} + N^{2} M - \frac{1}{3}N \) multiplications and \( \frac{1}{3}N^{3} + (M - \frac{1}{2})N^{2} - (M - \frac{1}{6})N \) additions. \( N \times N \) matrix multiplication and addition requires \( N^{2} (N - 1) \) and \( N^{2} \) additions and \( N^{3} \) and 0 multiplications, respectively.

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Author information

Authors and Affiliations

  1. Department of Telecommunications and Information Processing, Ghent University, St-Pietersnieuwstraat 41, 9000, Ghent, Belgium

    Dieter Fiems & Herwig Bruneel

  2. Department of Industrial Systems Engineering and Product Design, Ghent University, Technologiepark 903, 9052, Zwijnaarde, Belgium

    Stijn De Vuyst

Authors
  1. Dieter Fiems
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  2. Stijn De Vuyst
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  3. Herwig Bruneel
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Corresponding author

Correspondence to Dieter Fiems .

Editor information

Editors and Affiliations

  1. Faculty of Computing, Engineering and Science, University of South Wales, Pontypridd, United Kingdom

    Khalid Al-Begain

  2. ECMS, Nottingham, United Kingdom

    Andrzej Bargiela

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Fiems, D., De Vuyst, S., Bruneel, H. (2016). Flow-Level Packet Loss Analysis of a Markovian Bottleneck Buffer. In: Al-Begain, K., Bargiela, A. (eds) Seminal Contributions to Modelling and Simulation. Simulation Foundations, Methods and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-33786-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-33786-9_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33785-2

  • Online ISBN: 978-3-319-33786-9

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