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Flow-Level Packet Loss Analysis of a Markovian Bottleneck Buffer

  • Dieter FiemsEmail author
  • Stijn De Vuyst
  • Herwig Bruneel
Chapter
Part of the Simulation Foundations, Methods and Applications book series (SFMA)

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.

Keywords

Packet loss ratio Packet flow Queueing system 

References

  1. 1.
    Ait-Hellal O, Altman E, Jean-Marie A, Kurkova I (1999) On loss probabilities in presence of redundant packets and several traffic sources. Perform Eval 36–37:485–518CrossRefzbMATHGoogle Scholar
  2. 2.
    Alouf S, Nain P, Towsley D (2001) Inferring network characteristics via moment-based estimators. Proc INFOCOM 2001:1045–1054Google Scholar
  3. 3.
    Altman E, Jean-Marie A (1998) Loss probabilities for messages with redundant packets feeding a finite buffer. IEEE J Select Areas Commun 16(5):778–787CrossRefGoogle Scholar
  4. 4.
    Bratiychuk M, Chydzinski A (2009) On the loss process in a batch arrival queue. Appl Math Model 33(9):3565–3577MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Cidon I, Khamisy A, Sidi M (1993) Analysis of packet loss processes in high speed networks. IEEE Trans Inf Theory IT-39(1):98–108Google Scholar
  6. 6.
    Dán G, Fodor V, Karlsson G (2006) On the effects of the packet size distribution on the packet loss process. Telecommun Syst 32(1):31–53CrossRefzbMATHGoogle Scholar
  7. 7.
    Dán G, Fodor V, Karlsson G (2006) On the effects of the packet size distribution on FEC performance. Comput Netw 50(8):1104–1129CrossRefzbMATHGoogle Scholar
  8. 8.
    Dube P, Ait-Hellal O, Altman E (2003) On loss probabilities in presence of redundant packets with random drop. Perform Eval 52(3–4):147–167CrossRefzbMATHGoogle Scholar
  9. 9.
    Fiems D, Bruneel H (2005) On higher-order packet loss characteristics. In: Proceedings of the 2005 networking and electronic commerce research conference, Riva del Garda, ItalyGoogle Scholar
  10. 10.
    Fiems D, De Vuyst S, Wittevrongel S, Bruneel H (2009) Packet loss characteristics for M/G/1/N queueing systems. Ann Oper Res 170(1):113–131MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Fiems D, De Vuyst S, Wittevrongel S, Bruneel H (2009) An analytic study of a scalable video buffer. Telecommun Syst 41(1):25–36CrossRefGoogle Scholar
  12. 12.
    Frossard P (2001) FEC performance in multimedia streaming. IEEE Commun Lett 5(3):122–124CrossRefGoogle Scholar
  13. 13.
    Gravey A, Hébuterne G (1992) Simultaneity in discrete-time single server queues with Bernoulli inputs. Perform Eval 14:123–131MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gurewitz O, Sidi M, CidonI I (2000) The ballot theorem strikes again: packet loss process distribution. IEEE Trans Inf Theory 46(7):2588–2595MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Hadar O, Huber M, Huber R, Shmueli R (2004) Quality measurements for compressed video transmitted over a lossy packet network. Opt Eng 43(2):506–520CrossRefGoogle Scholar
  16. 16.
    Inoue Y, Takine T (2015) The M/D/1 + D queue has the minimum loss probability among M/G/1 + G queues. Oper Res Lett 43(6):629–632MathSciNetCrossRefGoogle Scholar
  17. 17.
    Inoue Y, Takine T (2015) Analysis of the loss probability in the M/G/1 + G queue. Queue Syst 80(4):363–386MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Jelenković P (1999) Subexponential loss rates in a GI/GI/1 queue with applications. Queue Syst 33:91–123Google Scholar
  19. 19.
    Kim H, Schroff N (2001) Loss probability calculations and asymptotic analysis for finite buffer multiplexers. IEEE/ACM Trans Netw 9(6):755–768CrossRefGoogle Scholar
  20. 20.
    Kim C, Dudin S, Klimenok V (2009) The MAP/PH/1/N queue with flows of customers as a model for traffic control in telecommunication networks. Perform Eval 66:564–579CrossRefGoogle Scholar
  21. 21.
    Kumazoe K, Kawahara K, Takine T, Oie Y (1997) Analysis of packet loss in transport layer over ATM networks. Int J Commun Syst 10:181–192CrossRefGoogle Scholar
  22. 22.
    Latouche G, Ramaswami V (1999) Introduction to matrix analytic methods in stochastic modeling. Series on statistics and applied probability. ASA-SIAMGoogle Scholar
  23. 23.
    Lin GC, Suda T, Ishizaki F (2005) Loss probability for a finite buffer multiplexer with the M/G/ input process. Telecommun Syst 29(3):181–197CrossRefGoogle Scholar
  24. 24.
    Michiel H, Laevens K (1997) Teletraffic engineering in a broad-band era. Proc IEEE 85(12):2007–2033CrossRefGoogle Scholar
  25. 25.
    Nardelli PHJ, Kountouris M, Cardieri P, Latva-aho M (2014) Throughput optimization in wireless networks under stability and packet loss constraints. IEEE Trans Mob Comput 13(8):1883–1895CrossRefGoogle Scholar
  26. 26.
    Pihlsgard M (2005) Loss rate asymptotics in a GI/G/1 queue with finite buffer. Stoch Models 21(4):913–931MathSciNetCrossRefGoogle Scholar
  27. 27.
    Schulzrinne H, Kurose J, Towsley D (1992) Loss correlation for queues with burtsty input streams. Proc IEEE ICC 219–224Google Scholar
  28. 28.
    Sheng H, Li S (1994) Spectral analysis of packet loss rate at a statistical multiplexer for multimedia services. IEEE/ACM Trans Network 2(1):53–65CrossRefGoogle Scholar
  29. 29.
    Steyaert B, Xiong Y, Bruneel H (1997) An efficient solution technique for discrete-time queues fed by heterogeneous traffic. Int J Commun Syst 10:73–86CrossRefGoogle Scholar
  30. 30.
    Takagi H (1993) Queueing analysis. Finite systems, vol 2. North-HollandGoogle Scholar
  31. 31.
    Takine T, Suda T, Hasegawa T (1995) Cell loss and output process analysis of a finite-buffer discrete-time ATM queueing system with correlated arrivals. IEEE Trans Commun 43:1022–1037CrossRefGoogle Scholar
  32. 32.
    Verscheure O, Garcia X, Karlsson G, Hubaux J (1998) User-oriented QoS in packet video delivery. IEEE Netw Mag 12:12–21CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Telecommunications and Information ProcessingGhent UniversityGhentBelgium
  2. 2.Department of Industrial Systems Engineering and Product DesignGhent UniversityZwijnaardeBelgium

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