Towards an analytical tool for performance modelling of ATM networks by decomposition

  • Gerhard Haßlinger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1245)


The analysis of open queueing networks by decomposition has developed to include more detailed and generalized representation forms of traffic. We investigate this method concerning its preconditions and requirements for ATM network modelling. We use discrete time semi-Markovian processes (SMP) to characterize traffic with short-term as well as long-term autocorrelation, and to evaluate the performance of ATM switches with non-renewal input. Basic results are summarized for the autocorrelation function of semi-Markov processes, which show how to represent autocorrelated traffic by an adequate SMP model of limited size.


ATM networks semi-Markov processes SMP/G/1 analysis in discrete time autocorrelation function self-similar traffic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G.R. Bitran and S. Dasu, A review of open queueing network models of manufacturing systems, Queueing Systems 12 (1992) 95–134.CrossRefMathSciNetGoogle Scholar
  2. [2]
    G.R. Bitran and S. Dasu, Approximating nonrenewal processes by Markov chains: Use of super-Erlang (SE) chains, Opsn. Res. 41 (1993) 903–923.Google Scholar
  3. [3]
    W. Ding, A unified correlated input process model for telecommunication networks, Proc. 13. Internat. Teletraffic Congress, Copenhagen, eds. A. Jensen and V.B. Iversen (1991) 539–544.Google Scholar
  4. [4]
    K.M. Elsayed, On the superposition of discrete-time Markov renewal processes and application to statistical multiplexing of bursty traffic sources, Proc. IEEE GLOBECOM (1994) 1113–1117.Google Scholar
  5. [5]
    W.K. Grassmann and J.L. Jain, Numerical solutions of the waiting time distribution and idle time distribution of the arithmetic GI/G/1 queue, Operations Research 37 (1989) 141–150.Google Scholar
  6. [6]
    G. Haßlinger, A polynomial factorization approach to the discrete time GI/G/1/(N) queue size distribution, Performance Evaluation 23 (1995) 217–240.CrossRefGoogle Scholar
  7. [7]
    G. Haßlinger, Semi-Markovian modelling and performance analysis of variable rate traffic in ATM networks, to appear in Telecommunication Systems, selected paper issue of the 3. INFORMS Telecom. Conf.Google Scholar
  8. [8]
    G. Haßilinger and M. Adam, Modelling and performance analysis of traffic in ATM networks including autocorrelation, Proc. IEEE Infocom'96 Conference, San Francisco (1996) 1460–1467.Google Scholar
  9. [9]
    G. Haßlinger and E.S. Rieger, Analysis of open discrete time queueing networks: A refined decomposition approach, J. Opl. Res. Soc. 47 (1996) 640–653.Google Scholar
  10. [10]
    B.R. Haverkort, Approximate analysis of networks of Ph/Ph/1/K queues: Theory & tool support, Proc. Performance Tools/MMB '95, Lecture Notes in Comp. Sci. 977, Springer (1995) 239–253.Google Scholar
  11. [11]
    J.J. Hunter, Mathematical techniques of applied probability, Vol. 1/2, Academic Press, New York (1983).Google Scholar
  12. [12]
    M.A. Johnson, An empirical study of queueing approximations based on phase-type distributions, Commun. Statist.-Stochastic Models 9, (1993) 531–561.Google Scholar
  13. [13]
    P.J. Kühn, Approximate analysis of general queueing networks by decomposition, IEEE Trans. on Com. COM-27 (1979) 113–126.CrossRefGoogle Scholar
  14. [14]
    W.E. Leland, M.S. Taqqu, W. Millinger and D.V. Wilson, On the self-similar nature of ethernet traffic, IEEE/ACM Trasnsactions on Networking 2 (1994) 1–15.CrossRefGoogle Scholar
  15. [15]
    B. Maglaris, D. Anastassiou, P. Sen, G. Karlsson and J. Robbins, Performance Models of Statistical Multiplexing in Packet Video Communications, IEEE Trans. on Com. COM-36 (1988) 834–843.CrossRefGoogle Scholar
  16. [16]
    M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models, J. Hopkins (1981)Google Scholar
  17. [17]
    M. Parulekar and A. Makowski, Tail probabilities for a multiplexer with self-similar traffic, Proc. IEEE Infocom'96 Conference, San Francisco (1996) 1452–1459.Google Scholar
  18. [18]
    V. Paxson and S. Floyd, Wide area traffic: The failure of Poisson modelling, IEEE/ACM Trasnsactions on Networking 3 (1995) 226–244.CrossRefGoogle Scholar
  19. [19]
    B. Pourbabai, Tandem behaviour of a telecommunication system with repeated calls: A Markovian case with buffers, J. Opl. Res. Soc. 40 (1989) 671–680.Google Scholar
  20. [20]
    S.V. Raghavan, D. Vasukiammaiyar and G. Haring, Hierarchical approach to building generative networkload models, Computer Networks and ISDN Systems 27 (1991) 1193–1206.CrossRefGoogle Scholar
  21. [21]
    E.S. Rieger and G. Haßlinger, An analytical solution to the discrete time single server queue with semi-Markovian arrivals, Queueing Systems 18 (1994) 69–105.CrossRefGoogle Scholar
  22. [22]
    F. Schwarzkopf, Cell scattering among bursty ATM traffic on virtual circuits and paths (in german) diploma thesis, TH Darmstadt (1995).Google Scholar
  23. [23]
    B. Sengupta, The semi-Markovian queue: Theory and applications, Commun. Statist.-Stochastic Models 6 (1990) 383–413.Google Scholar
  24. [24]
    K. Sriram and W. Whitt, Characterizing superposition arrival processes in packet multiplexers for voice and data, IEEE J. Sel. Areas in Com. SAC-4 (1986) 833–846.CrossRefGoogle Scholar
  25. [25]
    H.C. Tijms, Heuristics for the loss probability in finite-buffer queues, Proc. Conf. on Appl. Prob. in Engineering, Computer and Comm. Sciences, Paris (1993) 156–157.Google Scholar
  26. [26]
    W. Whitt, The queueing network analyser, Bell Syst. Techn. J. 62 (1983) 2779–2843.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Gerhard Haßlinger
    • 1
  1. 1.TH DarmstadtDarmstadtGermany

Personalised recommendations